The Experts below are selected from a list of 8337 Experts worldwide ranked by ideXlab platform
Vern I. Paulsen - One of the best experts on this subject based on the ideXlab platform.
-
equivariant maps and Bimodule projections
Journal of Functional Analysis, 2006Co-Authors: Vern I. PaulsenAbstract:We construct a counterexample to Solel's [B. Solel, Contractive projections onto Bimodules of von Neumann algebras, J. London Math. Soc. 45 (2) (1992) 169–179] conjecture that the range of any contractive, idempotent, MASA Bimodule map on B(H) is necessarily a ternary subalgebra. Our construction reduces this problem to an analogous problem about the ranges of idempotent maps that are equivariant with respect to a group action. Such maps are important to understand Hamana's theory [M. Hamana, Injective envelopes of C∗-dynamical systems, Tohoku Math. J. 37 (1985) 463–487] of G-injective operator spaces and G-injective envelopes.
-
ON THE RANGES OF Bimodule PROJECTIONS
Canadian Mathematical Bulletin, 2005Co-Authors: A Katavolos, Vern I. PaulsenAbstract:We develop a symbol calculus for normal Bimodule maps over a masa that is the natural analogue of the Schur product theory. Using this calculus we are easily able to give a complete description of the ranges of contractive normal Bimodule idempotents that avoids the theory of J*-algebras. We prove that if P is a normal Bimodule idempotent and ||P|| < 2/sqrt{3} then P is a contraction. We finish with some attempts at extending the symbol calculus to non-normal maps.
-
Multipliers of operator spaces, and the injective envelope
arXiv: Operator Algebras, 1999Co-Authors: David P Blecher, Vern I. PaulsenAbstract:We study the injective envelope I(X) of an operator space X, showing amongst other things that it is a self-dual C$^*-$module. We describe the diagonal corners of the injective envelope of the canonical operator system associated with X. We prove that if X is an operator $A-B$-Bimodule, then A and B can be represented completely contractively as subalgebras of these corners. Thus, the operator algebras that can act on X are determined by these corners of I(X) and consequently Bimodules actions on X extend naturally to actions on I(X). These results give another characterization of the multiplier algebra of an operator space, which was introduced by the first author, and a short proof of a recent characterization of operator modules, and a related result. As another application, we extend Wittstock's module map extension theorem, by showing that an operator $A-B$-Bimodule is injective as an operator $A-B$-Bimodule if and only if it is injective as an operator space.
Alan Hopenwasser - One of the best experts on this subject based on the ideXlab platform.
-
The spectral theorem for Bimodules in higher rank graph $C\sp *$-algebras
Illinois Journal of Mathematics, 2005Co-Authors: Alan HopenwasserAbstract:In this note we extend the spectral theorem for Bimodules to the higher rank graph C∗-algebra context. Under the assumption that the graph is row finite and has no sources, we show that a Bimodule over a natural abelian subalgebra is determined by its spectrum iff it is generated by the Cuntz-Krieger partial isometries which it contains iff the Bimodule is invariant under the gauge automorphisms. We also show that the natural abelian subalgebra is a masa iff the higher rank graph satisfies an aperiodicity condition.
-
The Spectral Theorem for Bimodules in Higher Rank Graph C*-algebras
arXiv: Operator Algebras, 2005Co-Authors: Alan HopenwasserAbstract:In this note we extend the spectral theorem for Bimodules to the higher rank graph C*-algebra context. Under the assumption that the graph is row finite and has no sources, we show that a Bimodule over a natural abelian subalgebra is determined by its spectrum iff it is generated by the Cuntz-Krieger partial isometries which it contains iff the Bimodule is invariant under the gauge automorphisms. We also show that the natural abelian subalgebra is a masa iff the higher rank graph satisfies an aperiodicity condition.
A Katavolos - One of the best experts on this subject based on the ideXlab platform.
-
ON THE RANGES OF Bimodule PROJECTIONS
Canadian Mathematical Bulletin, 2005Co-Authors: A Katavolos, Vern I. PaulsenAbstract:We develop a symbol calculus for normal Bimodule maps over a masa that is the natural analogue of the Schur product theory. Using this calculus we are easily able to give a complete description of the ranges of contractive normal Bimodule idempotents that avoids the theory of J*-algebras. We prove that if P is a normal Bimodule idempotent and ||P|| < 2/sqrt{3} then P is a contraction. We finish with some attempts at extending the symbol calculus to non-normal maps.
-
rank one subspaces of Bimodules over maximal abelian selfadjoint algebras
Journal of Functional Analysis, 1998Co-Authors: J A Erdos, A Katavolos, V S ShulmanAbstract:Spaces of operators that are left and right modules over maximal abelian selfadjoint algebras (masa Bimodules for short) are natural generalizations of algebras with commutative subspace lattices. This paper is concerned with density properties of finite rank operators and of various classes of compact operators in such modules. It is shown that every finite rank operator of a norm closed masa Bimodule M is in the trace norm closure of the rank one subspace of M. An important consequence is that the rank one subspace of a strongly reflexive masa Bimodule (that is, one which is the reflexive hull of its rank one operators) is dense in the module in the weak operator topology. However, in contrast to the situation for algebras, it is shown that such density need not hold in the ultraweak topology. A new method of representing masa Bimodules is introduced. This uses a novel concept of anω-topology. With the appropriate notion ofω-support, a correspondence is established between reflexive masa Bimodules and theirω-supports. It is shown that, if a C2-closed masa Bimodule contains a trace class operator then it must contain rank one operators; indeed, every such operator is in the C2-norm closure of the rank one subspace of the module. Consequently the weak closure of any masa Bimodule of trace class operators is strongly reflexive. However, the trace norm closure of the rank one subspace need not contain all trace class operators of the module. Also, it is shown that there exists a CSL algebra which contains no trace class operators yet contains an operator belonging to Cpfor allp>1. From this it follows that a transitive Bimodule spanned by the rank one operators it contains need not be dense in Cpfor 1⩽p<∞. As an application, it is shown that there exists a commutative subspace lattice L such that L is non-synthetic but every weakly closed algebra which contains a masa and has invariant lattice L coincides with Alg L.
Ivan G. Todorov - One of the best experts on this subject based on the ideXlab platform.
-
Ranges of Bimodule projections and reflexivity
Journal of Functional Analysis, 2012Co-Authors: G. K. Eleftherakis, Ivan G. TodorovAbstract:Abstract We develop a general framework for reflexivity in dual Banach spaces, motivated by the question of when the weak ⁎ closed linear span of two reflexive masa-Bimodules is automatically reflexive. We establish an affirmative answer to this question in a number of cases by examining two new classes of masa-Bimodules, defined in terms of ranges of masa-Bimodule projections. We give a number of corollaries of our results concerning operator and spectral synthesis, and show that the classes of masa-Bimodules we study are operator synthetic if and only if they are strong operator Ditkin.
-
Spectral synthesis and masa-Bimodules
arXiv: Operator Algebras, 2002Co-Authors: Ivan G. TodorovAbstract:Generalizing a result of Arveson on finite width CSL algebras, we prove that finite width masa-Bimodules satisfy spectral synthesis. Introducing a new class of masa-Bimodules, we show that there exists a non-synthetic masa-Bimodule, such that the maximal algebras over which it is a Bimodule, are synthetic.
-
Bimodules over next algebras and Deddens' Theorem
1997Co-Authors: Ivan G. TodorovAbstract:We generalize Deddens' theorem for nest algebras in the case of w*-closed nest algebras Bimodules. For each such Bimodule, we introduce a norm closed sub-Bimodule of it, which corresponds to the radical of a nest algebra and describe it in a number of ways, generalizing known facts about nest algebras.
Joost Vercruysse - One of the best experts on this subject based on the ideXlab platform.
-
Quasi-Frobenius functors. Applications
Communications in Algebra, 2010Co-Authors: F. Castano Iglesias, C. Nǎstǎsescu, Joost VercruysseAbstract:We investigate functors between abelian categories having a left adjoint and a right adjoint that are similar (these functors are called quasi-Frobenius functors). We introduce the notion of a quasi-Frobenius Bimodule and give a characterization of these Bimodules in terms of quasi-Frobenius functors. Some applications to corings and graded rings are presented. In particular, the concept of quasi-Frobenius homomorphism of corings is introduced. Finally, a version of the endomorphism ring Theorem for quasi-Frobenius extensions in terms of corings is obtained.
-
Bimodule herds
2008Co-Authors: Tomasz Brzeziński, Joost VercruysseAbstract:The notion of a Bimodule herd is introduced and studied. A Bimodule herd consists of a $B$-$A$ Bimodule, its formal dual, called a pen, and a map, called a shepherd, which satisfies untiality and coassociativity conditions. It is shown that every Bimodule herd gives rise to a pair of corings and coactions. If, in addition, a Bimodule herd is tame i.e. it is faithfully flat and a progenerator, then these corings are associated to entwining structures; the Bimodule herd is a Galois comodule of these corings. The notion of a bicomodule coherd is introduced as a formal dualisation of the definition of a Bimodule herd. Every bicomodule coherd defines a pair of (non-unital) rings. It is shown that a tame $B$-$A$ Bimodule herd defines a bicomodule coherd, and sufficient conditions for the derived rings to be isomorphic to $A$ and $B$ are discussed. The composition of Bimodule herds via the tensor product is outlined. The notion of a Bimodule herd is illustrated by the example of Galois co-objects of a commutative, faithfully flat Hopf algebra.
-
Quasi-Frobenius functors. Applications
arXiv: Rings and Algebras, 2006Co-Authors: F. Castano Iglesias, C. Nastasescu, Joost VercruysseAbstract:We investigate functors between abelian categories having a left adjoint and a right adjoint that are \emph{similar} (these functors are called \emph{quasi-Frobenius functors}). We introduce the notion of a \emph{quasi-Frobenius Bimodule} and give a characterization of these Bimodules in terms of quasi-Frobenius functors. Some applications to corings and graded rings are presented. In particular, the concept of quasi-Frobenius homomorphism of corings is introduced. Finally, a version of the endomorphism ring Theorem for quasi-Frobenius extensions in terms of corings is obtained.
