scholarly journals Equivalence classes of invariant subspaces in nonselfadjoint crossed products

1984 ◽  
Vol 20 (6) ◽  
pp. 1119-1138
Author(s):  
Michael McAsey ◽  
Paul S. Muhly ◽  
Kichi-Suke Saito
Keyword(s):  
Invariant Subspaces ◽  
Equivalence Classes ◽  
Crossed Products

scholarly journals EPSILON-STRONGLY GROUPOID-GRADED RINGS, THE PICARD INVERSE CATEGORY AND COHOMOLOGY

2019 ◽  
Vol 62 (1) ◽  
pp. 233-259 ◽  
Author(s):  
PATRIK NYSTEDT ◽  
JOHAN ÖINERT ◽  
HÉCTOR PINEDO
Keyword(s):  
Cohomology Group ◽  
Equivalence Classes ◽  
Crossed Products ◽  
Graded Rings ◽  
Classical Construction

AbstractWe introduce the class of partially invertible modules and show that it is an inverse category which we call the Picard inverse category. We use this category to generalize the classical construction of crossed products to, what we call, generalized epsilon-crossed products and show that these coincide with the class of epsilon-strongly groupoid-graded rings. We then use generalized epsilon-crossed groupoid products to obtain a generalization, from the group-graded situation to the groupoid-graded case, of the bijection from a certain second cohomology group, defined by the grading and the functor from the groupoid in question to the Picard inverse category, to the collection of equivalence classes of rings epsilon-strongly graded by the groupoid.

Strong Morita Equivalence for Heisenberg C*-Algebras and the Positive Cones of Their K 0-Groups

1988 ◽  
Vol 40 (04) ◽  
pp. 833-864 ◽  
Author(s):  
Judith A. Packer
Keyword(s):  
Heisenberg Group ◽  
Morita Equivalence ◽  
Equivalence Classes ◽  
Crossed Products ◽  
C Algebras ◽  
Projective Representations ◽  
Discrete Heisenberg Group ◽  
Strong Morita Equivalence

In [14] we began a study of C*-algebras corresponding to projective representations of the discrete Heisenberg group, and classified these C*-algebras up to *-isomorphism. In this sequel to [14] we continue the study of these so-called Heisenberg C*-algebras, first concentrating our study on the strong Morita equivalence classes of these C*-algebras. We recall from [14] that a Heisenberg C*-algebra is said to be of class i, i ∊ {1, 2, 3}, if the range of any normalized trace on its K 0 group has rank i as a subgroup of R; results of Curto, Muhly, and Williams [7] on strong Morita equivalence for crossed products along with the methods of [21] and [14] enable us to construct certain strong Morita equivalence bimodules for Heisenberg C*-algebras.

scholarly journals On the symmetric algebra of quotients of a C*-algebra

1990 ◽  
Vol 32 (3) ◽  
pp. 377-379 ◽  
Author(s):  
Pere Ara
Keyword(s):  
Galois Theory ◽  
Semiprime Ring ◽  
Equivalence Classes ◽  
Crossed Products ◽  
Prime Rings ◽  
C Algebra ◽  
Essential Ideal ◽  
Module Homomorphism ◽  
Semiprime Rings ◽  
Ring Of Quotients

Let R be a semiprime ring (possibly without 1). The symmetric ring of quotients of R is defined as the set of equivalence classes of essentially defined double centralizers (ƒ, g) on R; see [1], [8]. So, by definition, ƒ is a left R-module homomorphism from an essential ideal I of R into R, g is a right R-module homomorphism from an essential ideal J of R into R, and they satisfy the balanced condition ƒ(x)y = xg(y) for x ∈ Iand y ∈ J. This ring was used by Kharchenko in his investigations on the Galois theory of semiprime rings [4] and it is also a useful tool for the study of crossed products of prime rings [7]. We denote the symmetric ring of quotients of a semiprime ring R by Q(R).

Generalized interpolation in finite maximal subdiagonal algebras

1995 ◽  
Vol 117 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Kichi-Suke Saito
Keyword(s):  
Selfadjoint Operator ◽  
Operator Algebras ◽  
Invariant Subspaces ◽  
Factorization Theorem ◽  
Crossed Products ◽  
Analytic Operator ◽  
Nest Algebras ◽  
Function Algebras ◽  
Reflexive Algebras

Non-selfadjoint operator algebras have been studied since the paper of Kadison and Singer in 1960. In [1], Arveson introduced the notion of subdiagonal algebras as the generalization of weak *-Dirichlet algebras and studied the analyticity of operator algebras. After that, we have many papers about non-selfadjoint algebras in this direction: nest algebras, CSL algebras, reflexive algebras, analytic operator algebras, analytic crossed products and so on. Since the notion of subdiagonal algebras is the analogue of weak *-Dirichlet algebras, subdiagonal algebras have many fruitful properties from the theory of function algebras. Thus, we have several attempts in this direction: Beurling–Lax–Halmos theorem for invariant subspaces, maximality, factorization theorem and so on.

scholarly journals Nonselfadjoint crossed products (invariant subspaces and maximality)

1979 ◽  
Vol 248 (2) ◽  
pp. 381-381 ◽  
Author(s):  
Michael McAsey ◽  
Paul S. Muhly ◽  
Kichi-Suke Saito
Keyword(s):  
Invariant Subspaces ◽  
Crossed Products
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