The Experts below are selected from a list of 22032 Experts worldwide ranked by ideXlab platform
Vladimir G. Troitsky - One of the best experts on this subject based on the ideXlab platform.
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FINITELY STRICTLY Singular OperatorS BETWEEN JAMES SPACES
Journal of Functional Analysis, 2009Co-Authors: Isabelle Chalendar, Alexey I. Popov, Emmanuel Fricain, Dan Timotin, Vladimir G. TroitskyAbstract:Abstract An Operator T : X → Y between Banach spaces is said to be finitely strictly Singular if for every e > 0 there exists n such that every subspace E ⊆ X with dim E ⩾ n contains a vector x such that ‖ T x ‖ e ‖ x ‖ . We show that, for 1 ⩽ p q ∞ , the formal inclusion Operator from J p to J q is finitely strictly Singular. As a consequence, we obtain that the strictly Singular Operator with no invariant subspaces constructed by C. Read is actually finitely strictly Singular. These results are deduced from the following fact: if k ⩽ n then every k-dimensional subspace of R n contains a vector x with ‖ x ‖ l ∞ = 1 such that x m i = ( − 1 ) i for some m 1 ⋯ m k .
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INVARIANT SUBSPACES OF POSITIVE STRICTLY Singular OperatorS ON BANACH LATTICES
Journal of Mathematical Analysis and Applications, 2008Co-Authors: Julio Flores, Pedro Tradacete, Vladimir G. TroitskyAbstract:It is shown that every positive strictly Singular Operator T on a Banach lattice satisfying certain conditions is AM-compact and has invariant subspaces. Moreover, every positive Operator commuting with T has an invariant subspace. It is also proved that on such spaces the product of a disjointly strictly Singular and a regular AM-compact Operator is strictly Singular. Finally, we prove that on these spaces the known invariant subspace results for compact-friendly Operators can be extended to strictly Singular-friendly Operators.
Andreas Axelsson - One of the best experts on this subject based on the ideXlab platform.
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Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I
Inventiones mathematicae, 2011Co-Authors: Pascal Auscher, Andreas AxelssonAbstract:We develop new solvability methods for divergence form second order, real and complex, elliptic systems above Lipschitz graphs, with L _2 boundary data. The coefficients A may depend on all variables, but are assumed to be close to coefficients A _0 that are independent of the coordinate transversal to the boundary, in the Carleson sense ‖ A − A _0‖_ C defined by Dahlberg. We obtain a number of a priori estimates and boundary behaviour results under finiteness of ‖ A − A _0‖_ C . Our methods yield full characterization of weak solutions, whose gradients have L _2 estimates of a non-tangential maximal function or of the square function, via an integral representation acting on the conormal gradient, with a Singular Operator-valued kernel. Also, the non-tangential maximal function of a weak solution is controlled in L _2 by the square function of its gradient. This estimate is new for systems in such generality, and even for real non-symmetric equations in dimension 3 or higher. The existence of a proof a priori to well-posedness, is also a new fact. As corollaries, we obtain well-posedness of the Dirichlet, Neumann and Dirichlet regularity problems under smallness of ‖ A − A _0‖_ C and well-posedness for A _0, improving earlier results for real symmetric equations. Our methods build on an algebraic reduction to a first order system first made for coefficients A _0 by the two authors and A. McIntosh in order to use functional calculus related to the Kato conjecture solution, and the main analytic tool for coefficients A is an operational calculus to prove weighted maximal regularity estimates.
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Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I
2010Co-Authors: Pascal Auscher, Andreas AxelssonAbstract:We develop new solvability methods for divergence form second order, real and complex, elliptic systems above Lipschitz graphs, with $L_2$ boundary data. The coefficients $A$ may depend on all variables, but are assumed to be close to coefficients $A_0$ that are independent of the coordinate transversal to the boundary, in the Carleson sense $\|A-A_0\|_C$ defined by Dahlberg. We obtain a number of {\em a priori} estimates and boundary behaviour results under finiteness of $\|A-A_0\|_C$. Our methods yield full characterization of weak solutions, whose gradients have $L_2$ estimates of a non-tangential maximal function or of the square function, via an integral representation acting on the conormal gradient, with a Singular Operator-valued kernel. Also, the non-tangential maximal function of a weak solution is controlled in $L_2$ by the square function of its gradient. This estimate is new for systems in such generality, and even for real non-symmetric equations in dimension $3$ or higher. The existence of a proof {\em a priori} to well-posedness, is also a new fact. As corollaries, we obtain well-posedness of the Dirichlet, Neumann and Dirichlet regularity problems under smallness of $\|A-A_0\|_C$ and well-posedness for $A_0$, improving earlier results for real symmetric equations. Our methods build on an algebraic reduction to a first order system first made for coefficients $A_0$ by the two authors and A. McIntosh in order to use functional calculus related to the Kato conjecture solution, and the main analytic tool for coefficients $A$ is an operational calculus to prove weighted maximal regularity estimates.
Radjesvarane Alexandre - One of the best experts on this subject based on the ideXlab platform.
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integral estimates for a linear Singular Operator linked with boltzmann Operators part ii high Singularities 1 le nu 2
Kinetic and Related Models, 2008Co-Authors: Radjesvarane AlexandreAbstract:In this work, we show that integral estimates for a linear Operator linked with Boltzmann quadratic Operator considered in [1] can also be obtained for the case of higher Singularities. Some estimates proven in this earlier work are improved, as in particular, we do not need any regularity with respect to the first function.
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integral estimates for a linear Singular Operator linked with the boltzmann Operator part i small Singularities o v 1
Indiana University Mathematics Journal, 2006Co-Authors: Radjesvarane AlexandreAbstract:We give precise integral estimates for a linear Operator linked with Boltzmann quadratic Operator. This is done for Singular cross-sections. We show Calderon-Zygmund and commutators type estimates. In particular, these estimates can be used to deduce some functional properties of Boltzmann Operator itself.
Pascal Auscher - One of the best experts on this subject based on the ideXlab platform.
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Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I
Inventiones mathematicae, 2011Co-Authors: Pascal Auscher, Andreas AxelssonAbstract:We develop new solvability methods for divergence form second order, real and complex, elliptic systems above Lipschitz graphs, with L _2 boundary data. The coefficients A may depend on all variables, but are assumed to be close to coefficients A _0 that are independent of the coordinate transversal to the boundary, in the Carleson sense ‖ A − A _0‖_ C defined by Dahlberg. We obtain a number of a priori estimates and boundary behaviour results under finiteness of ‖ A − A _0‖_ C . Our methods yield full characterization of weak solutions, whose gradients have L _2 estimates of a non-tangential maximal function or of the square function, via an integral representation acting on the conormal gradient, with a Singular Operator-valued kernel. Also, the non-tangential maximal function of a weak solution is controlled in L _2 by the square function of its gradient. This estimate is new for systems in such generality, and even for real non-symmetric equations in dimension 3 or higher. The existence of a proof a priori to well-posedness, is also a new fact. As corollaries, we obtain well-posedness of the Dirichlet, Neumann and Dirichlet regularity problems under smallness of ‖ A − A _0‖_ C and well-posedness for A _0, improving earlier results for real symmetric equations. Our methods build on an algebraic reduction to a first order system first made for coefficients A _0 by the two authors and A. McIntosh in order to use functional calculus related to the Kato conjecture solution, and the main analytic tool for coefficients A is an operational calculus to prove weighted maximal regularity estimates.
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Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I
2010Co-Authors: Pascal Auscher, Andreas AxelssonAbstract:We develop new solvability methods for divergence form second order, real and complex, elliptic systems above Lipschitz graphs, with $L_2$ boundary data. The coefficients $A$ may depend on all variables, but are assumed to be close to coefficients $A_0$ that are independent of the coordinate transversal to the boundary, in the Carleson sense $\|A-A_0\|_C$ defined by Dahlberg. We obtain a number of {\em a priori} estimates and boundary behaviour results under finiteness of $\|A-A_0\|_C$. Our methods yield full characterization of weak solutions, whose gradients have $L_2$ estimates of a non-tangential maximal function or of the square function, via an integral representation acting on the conormal gradient, with a Singular Operator-valued kernel. Also, the non-tangential maximal function of a weak solution is controlled in $L_2$ by the square function of its gradient. This estimate is new for systems in such generality, and even for real non-symmetric equations in dimension $3$ or higher. The existence of a proof {\em a priori} to well-posedness, is also a new fact. As corollaries, we obtain well-posedness of the Dirichlet, Neumann and Dirichlet regularity problems under smallness of $\|A-A_0\|_C$ and well-posedness for $A_0$, improving earlier results for real symmetric equations. Our methods build on an algebraic reduction to a first order system first made for coefficients $A_0$ by the two authors and A. McIntosh in order to use functional calculus related to the Kato conjecture solution, and the main analytic tool for coefficients $A$ is an operational calculus to prove weighted maximal regularity estimates.
César R. De Oliveira - One of the best experts on this subject based on the ideXlab platform.
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Quantum Singular Operator limits of thin Dirichlet tubes via Γ-convergence
Reports on Mathematical Physics, 2011Co-Authors: César R. De OliveiraAbstract:The Γ -convergence of lower bounded quadratic forms is used to study the Singular Operator limit of thin tubes (i.e. the vanishing of the cross-section diameter) of the Laplace Operator with Dinchlet boundary conditions; a procedure to obtain the effective Schrodinger Operator (in different subspaces) is proposed, generalizing recent results in case of compact tubes. Finally, after scaling curvature and torsion the limit of a broken line is briefly investigated.
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quantum Singular Operator limits of thin dirichlet tubes via gamma convergence
arXiv: Mathematical Physics, 2010Co-Authors: César R. De OliveiraAbstract:The $\Gamma$-convergence of lower bounded quadratic forms is used to study the Singular Operator limit of thin tubes (i.e., the vanishing of the cross section diameter) of the Laplace Operator with Dirichlet boundary conditions; a procedure to obtain the effective Schr\"odinger Operator (in different subspaces) is proposed, generalizing recent results in case of compact tubes. Finally, after scaling curvature and torsion the limit of a broken line is briefly investigated.
