On Non-Self-Adjoint Operator Algebras

1990 ◽  
Vol 110 (4) ◽  
pp. 915 ◽  
Author(s):  
Edward G. Effros ◽  
Zhong-Jin Ruan
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator

scholarly journals Hyers-Ulam-Rassias stability of (m, n)-Jordan derivations

2020 ◽  
Vol 18 (1) ◽  
pp. 1615-1624
Author(s):  
Guangyu An ◽  
Ying Yao
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator ◽  
Rassias Stability

Abstract In this paper, we study the Hyers-Ulam-Rassias stability of ( m , n ) (m,n) -Jordan derivations. As applications, we characterize ( m , n ) (m,n) -Jordan derivations on C ⁎ {C}^{\ast } -algebras and some non-self-adjoint operator algebras.

On the Structure of Certain Nest Algebra Modules

1987 ◽  
Vol 39 (6) ◽  
pp. 1405-1412
Author(s):  
G. J. Knowles
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator ◽  
Systematic Investigation ◽  
Unique Determination ◽  
Nest Algebra ◽  
Minimal Elements ◽  
Open Questions ◽  
Weakly Closed ◽  
Order Homomorphisms

Let be a nest algebra of operators on some Hilbert space H. Weakly closed -modules were first studied by J. Erdos and S. Power in [4]. It became apparent that many interesting classes of non self-adjoint operator algebras arise as just such a module. This paper undertakes a systematic investigation of the correspondence which arises between such modules and order homomorphisms from Lat into itself. This perspective provides a basis to answer some open questions arising from [4]. In particular, the questions concerning unique “determination” and characterization of maximal and minimal elements under this correspondence, are resolved. This is then used to establish when the determining homomorphism is unique.

scholarly journals Tensor products of non-self-adjoint operator algebras

1990 ◽  
Vol 20 (2) ◽  
pp. 331-350 ◽  
Author(s):  
V. PAULSEN ◽  
S. POWER
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator ◽  
Tensor Products

scholarly journals Classification of irreversible and reversible Pimsner operator algebras

2020 ◽  
Vol 156 (12) ◽  
pp. 2510-2535
Author(s):  
Adam Dor-On ◽  
Søren Eilers ◽  
Shirly Geffen
Keyword(s):  
Algebraic Structure ◽  
Operator Algebras ◽  
Directed Graphs ◽  
Adjoint Operator ◽  
Neumann Operator ◽  
Von Neumann ◽  
Shed Light

AbstractSince their inception in the 1930s by von Neumann, operator algebras have been used to shed light on many mathematical theories. Classification results for self-adjoint and non-self-adjoint operator algebras manifest this approach, but a clear connection between the two has been sought since their emergence in the late 1960s. We connect these seemingly separate types of results by uncovering a hierarchy of classification for non-self-adjoint operator algebras and $C^{*}$-algebras with additional $C^{*}$-algebraic structure. Our approach naturally applies to algebras arising from $C^{*}$-correspondences to resolve self-adjoint and non-self-adjoint isomorphism problems in the literature. We apply our strategy to completely elucidate this newly found hierarchy for operator algebras arising from directed graphs.

scholarly journals Isometries of non-self-adjoint operator algebras

1990 ◽  
Vol 90 (2) ◽  
pp. 284-305 ◽  
Author(s):  
Jonathan Arazy ◽  
Baruch Solel
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator

scholarly journals Operator algebras with a reduction property

2006 ◽  
Vol 80 (3) ◽  
pp. 297-315 ◽  
Author(s):  
James A. Gifford
Keyword(s):  
Hilbert Space ◽  
Banach Algebra ◽  
Invariant Subspace ◽  
Operator Algebras ◽  
Adjoint Operator ◽  
Compact Operators ◽  
Total Reduction ◽  
Reduction Property ◽  
Similarity Problem ◽  
Closed Invariant Subspace

AbstractGiven a representation θ: A → B(H) of a Banach algebra A on a Hilbert space H, H is said to have the reduction property as an A—module if every closed invariant subspace of H is complemented by a closed invariant subspace; A has the total reduction property if for every representation θ: A → B(H), H has the reduction property.We show that a C*—algebra has the total reduction property if and only if all its representations are similar to *—representations. The question of whether all C*-algebras have this property is the famous ‘similarity problem’ of Kadison.We conjecture that non-self-adjoint operator algebras with the total reduction property are always isomorphic to C*-algebras, and prove this result for operator algebras consisting of compact operators.

scholarly journals On commutative non-self-adjoint operator algebras

1974 ◽  
Vol 15 (1) ◽  
pp. 54-59 ◽  
Author(s):  
R. H. Kelly
Keyword(s):  
Hilbert Space ◽  
Operator Algebras ◽  
Adjoint Operator ◽  
Complex Hilbert Space ◽  
Special Case

A proof is given here of a theorem of Sarason [9, Theorem 2], the proof being valid in an arbitrary (non-separable) complex Hilbert space. Sarason's proof uses a theorem and lemma of Wermer which may both fail when the separability hypothesis is omitted [3]. By using a special case of Sarason's theorem and another result of Sarason [10, Lemma 1] a simplified and shortened proof is given of a result of Scroggs [11, Corollary 1].

scholarly journals A reduction theory for non-self-adjoint operator algebras

1976 ◽  
Vol 224 (2) ◽  
pp. 351-351 ◽  
Author(s):  
E. A. Azoff ◽  
C. K. Fong ◽  
F. Gilfeather
Keyword(s):  
Operator Algebras ◽  
Adjoint Operator ◽  
Reduction Theory
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