The Experts below are selected from a list of 252 Experts worldwide ranked by ideXlab platform
Roland Speicher - One of the best experts on this subject based on the ideXlab platform.
-
Resolvents of R- Diagonal Operators
Transactions of the American Mathematical Society, 2010Co-Authors: Uffe Haagerup, Todd Kemp, Roland SpeicherAbstract:We consider the resolvent (λ-a) -1 of any ℛ-Diagonal Operator a in a II 1 -factor. Our main theorem (Theorem 1.1) gives a universal asymptotic formula for the norm of such a resolvent. En route to its proof, we calculate the ℛ-transform of the Operator |λ - c| 2 where c is Voiculescu's circular Operator, and we give an asymptotic formula for the negative moments of |ℛ - a| 2 for any ℛ-Diagonal a. We use a mixture of complex analytic and combinatorial techniques, each giving finer information where the other can give only coarse detail. In particular, we introduce partition structure diagrams in Section 4, a new combinatorial structure arising in free probability.
-
Resolvents of R-Diagonal Operators
arXiv: Operator Algebras, 2008Co-Authors: Uffe Haagerup, Todd Kemp, Roland SpeicherAbstract:We consider the resolvent $(\lambda-a)^{-1}$ of any $R$-Diagonal Operator $a$ in a $\mathrm{II}_1$-factor. Our main theorem gives a universal asymptotic formula for the norm of such a resolvent. En route to its proof, we calculate the $R$-transform of the Operator $|\lambda-c|^2$ where $c$ is Voiculescu's circular Operator, and give an asymptotic formula for the negative moments of $|\lambda-a|^2$ for any $R$-Diagonal $a$. We use a mixture of complex analytic and combinatorial techniques, each giving finer information where the other can give only coarse detail. In particular, we introduce {\em partition structure diagrams}, a new combinatorial structure arising in free probability.
-
Continuous family of invariant subspaces for R–Diagonal Operators
Inventiones Mathematicae, 2001Co-Authors: Piotr Śniady, Roland SpeicherAbstract:We show that every R–Diagonal Operator x has a continuous family of invariant subspaces relative to the von Neumann algebra generated by x. This allows us to find the Brown measure of x and to find a new conceptual proof that Voiculescu’s S–transform is multiplicative. Our considerations base on a new concept of R–Diagonality with amalgamation, for which we give several equivalent characterizations.
Spiros A. Argyros - One of the best experts on this subject based on the ideXlab platform.
-
A weak Hilbert space with few symmetries
Comptes Rendus Mathematique, 2010Co-Authors: Spiros A. Argyros, Kevin Beanland, Theocharis RaikoftsalisAbstract:Abstract We construct a separable Banach space X w h with an unconditional basis that is a weak Hilbert space and no block subspace is linearly isomorphic to any of its proper subspaces. We prove that the space X w h satisfies these properties by showing it is strongly asymptotic l 2 and that every bounded linear Operator on X w h is a strictly singular perturbation of a Diagonal Operator with respect to the unit vector basis.
-
A weak Hilbert space with few symmetries
arXiv: Functional Analysis, 2009Co-Authors: Spiros A. Argyros, Kevin Beanland, Theocharis RaikoftsalisAbstract:We construct a weak Hilbert Banach space such that for every block subspace $Y$ every bounded linear Operator on Y is of the form D+S where S is a strictly singular Operator and D is a Diagonal Operator. We show that this yields a weak Hilbert space whose block subspaces are not isomorphic to any of their proper subspaces.
-
A CLASS OF BANACH SPACES WITH FEW NON STRICTLY SINGULAR OperatorS
Journal of Functional Analysis, 2005Co-Authors: Spiros A. Argyros, Jordi Lopez-abad, Stevo TodorcevicAbstract:We construct a family (Xγ) of reflexive Banach spaces with long (countable as well as uncountable) transfinite bases but with no unconditional basic sequences. The method we introduce to achieve this allows us to considerably control the structure of subspaces of the resulting spaces as well as to precisely describe the corresponding spaces on non-strictly singular Operators. For example, for every pair of countable ordinals γ,β, we are able to decompose every bounded linear Operator from Xγ to Xβ as the sum of a Diagonal Operator and an strictly singular Operator. We also show that every finite-dimensional subspace of any member Xγ of our class can be moved by and (4+ɛ)-isomorphism to essentially any region of any other member Xδ or our class. Finally, we find subspaces X of Xγ such that the Operator space L(X,Xγ) is quite rich but any bounded Operator T from X into X is a strictly singular pertubation of a scalar multiple of the identity.
Lixin Qian - One of the best experts on this subject based on the ideXlab platform.
-
Optimal algorithms for Diagonal Operators on N-widths in different computational setting
Analysis in Theory and Applications, 2007Co-Authors: Gensun Fang, Lixin QianAbstract:In this paper, we give some optimal algorithms for Diagonal Operator T from space lp (1 ≦ p ≦ 2) to l2 on n-widths in different computational setting.
Toka Diagana - One of the best experts on this subject based on the ideXlab platform.
-
Spectral Analysis for Finite Rank Perturbations of Diagonal Operators in non-Archimedean Hilbert Space ∗
P-Adic Numbers Ultrametric Analysis and Applications, 2014Co-Authors: Toka Diagana, R. Kerby, Teylama H. Miabey, F. RamarosonAbstract:In this paper we are concerned with the spectral analysis for some classes of finite rank perturbations of Diagonal Operators in the form, A = D + F, where D is a Diagonal Operator and F = u1 ⊗ v1 + u2 ⊗ v2 + … + um ⊗ vm is an Operator of finite rank in the non-archimedean Hilbert space \(\mathbb{E}_\omega \). Using the theory of Fredholm Operators in the non-archimedean setting and the concept of essential spectrum for linear Operators, we compute the spectrum of A. A few examples are given at the end of the paper to illustrate our main results.
-
Spectral analysis for finite rank perturbations of Diagonal Operators in non-archimedean Hilbert space
P-Adic Numbers Ultrametric Analysis and Applications, 2014Co-Authors: Toka Diagana, R. Kerby, Teylama H. Miabey, F. RamarosonAbstract:In this paper we are concerned with the spectral analysis for some classes of finite rank perturbations of Diagonal Operators in the form, A = D + F , where D is a Diagonal Operator and F = u _1 ⊗ v _1 + u _2 ⊗ v _2 + … + u _ m ⊗ v _ m is an Operator of finite rank in the non-archimedean Hilbert space $\mathbb{E}_\omega $ . Using the theory of Fredholm Operators in the non-archimedean setting and the concept of essential spectrum for linear Operators, we compute the spectrum of A . A few examples are given at the end of the paper to illustrate our main results.
-
Spectral analysis for rank-one perturbations of Diagonal Operators in non-archimedean Hilbert space
2009Co-Authors: Toka Diagana, George D. McnealAbstract:The paper is concerned with the spectral analysis for the class of linear Operators $A = D_\lambda + X \otimes Y$ in non-archimedean Hilbert space, where $D_\lambda$ is a Diagonal Operator and $X \otimes Y$ is a rank one Operator. The results of this paper turn out to be a generalization of those results obtained by Diarra.
Gensun Fang - One of the best experts on this subject based on the ideXlab platform.
-
Optimal algorithms for Diagonal Operators on N-widths in different computational setting
Analysis in Theory and Applications, 2007Co-Authors: Gensun Fang, Lixin QianAbstract:In this paper, we give some optimal algorithms for Diagonal Operator T from space lp (1 ≦ p ≦ 2) to l2 on n-widths in different computational setting.