The Ideal Structure of Certain Nonselfadjoint Operator Algebras

Peters, Justin R.

doi:10.2307/2001056

Cited by 11 publications

(17 citation statements)

References 3 publications

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“…In the case where G is discrete, our definition of A⋊ α Σ coincides with the one commonly appearing in the literature [11,12,30,31]. The same is true in the non-discrete case as well but that requires some explanation.…”

Section: Stable Isomorphisms Of Semicrossed Productsmentioning

confidence: 62%

“…We do this in an indirect way using Theorem 2.11 and the dynamical system (A ⊗ K(G, Σ, µ), G, α ⊗ Ad ρ) appearing in that theorem. This works for any abelian group admitting an ordered structure, not just discrete ones, and sheds new light on an old result of Peters [31,III.5. Theorem].…”

Section: Introductionmentioning

confidence: 57%

“…Starting with work of Arveson in the sixties [4,5], the study of semicrossed products by Z + (or other discrete semigroups) has been a central topic of investigation in operator algebra theory and has produced a steady stream of important results [8,12,11,9,20,30,31]. Quite recently, the authors of the present paper started studying crossed products of operator algebras [22], in connection with several problems in both selfadjoint and non-selfadjoint operator algebra theory.…”

Section: Introductionmentioning

confidence: 94%

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Crossed products of operator algebras: Applications of Takai duality

Katsoulis

Ramsey

2018

Journal of Functional Analysis

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Let (G, Σ) be an ordered abelian group with Haar measure µ, let (A, G, α) be a dynamical system and let A ⋊α Σ be the associated semicrossed product. Using Takai duality we establish a stable isomorphismwhere K(G, Σ, µ) denotes the compact operators in the CSL algebra Alg L(G, Σ, µ) and ρ denotes the right regular representation of G. We also show that there exists a complete lattice isomorphism between thêUsing Takai duality we also continue our study of the Radical for the crossed product of an operator algebra and we solve open problems stemming from the earlier work of the authors. Among others we show that the crossed product of a radical operator algebra by a compact abelian group is a radical operator algebra. We also show that the permanence of semisimplicity fails for crossed products by R. A final section of the paper is devoted to the study of radically tight dynamical systems, i.e., dynamical systems (A, G, α) for which the identity Rad(A ⋊α G) = (Rad A) ⋊α G persists. A broad class of such dynamical systems is identified.

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Section: Stable Isomorphisms Of Semicrossed Productsmentioning

confidence: 62%

Section: Introductionmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 94%

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Crossed products of operator algebras: Applications of Takai duality

Katsoulis

Ramsey

2018

Journal of Functional Analysis

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“…The representations of the form ϕ λ are enough to ensure semisimplicity of T + (C n ) a well known result for certain graph operator algebras, see [4], or [10], and semicrossed products, see [14]. We include the proof in this context for completeness, and since it is not difficult.…”

Section: Point Derivations On T + (C N )mentioning

confidence: 95%

Derivations for a class of matrix function algebras

Duncan

2007

Linear Algebra and its Applications

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We study a class of matrix function algebras, here denoted T + (C n ). We introduce a notion of point derivations, and classify the point derivations for certain finite dimensional representations of T + (C n ). We use point derivations and information about n × n matrices to show that every T + (C n )-valued derivation on T + (C n ) is inner.2000 Mathematics Subject Classification. 47L75, 46H35.

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“…Proof. Since a is a homomorphism, it is easy to see that d is as well since m+n i = EE i=o j=o By using the representation IIz of elements in Z""" Xq C(T) given in Peters [Pet2], Thus, a is isometric on a dense subset of 21q. That a is one-to-one and onto is also clear since Q is invertible.…”

Section: The Maximal Ideal Space Of Z+ Xa 4(d)mentioning

confidence: 99%

Hilbert modules over semicrossed products of the disk algebra

Buske

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This manuscript has been reproduced from the microfilm master. UMI fihns the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter &ce, while others may be from ai^ type of computer printer.The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction.In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.Oversize materials (e.g., m^s, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book.

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The Ideal Structure of Certain Nonselfadjoint Operator Algebras

Cited by 11 publications

References 3 publications

Crossed products of operator algebras: Applications of Takai duality

Crossed products of operator algebras: Applications of Takai duality

Derivations for a class of matrix function algebras

Hilbert modules over semicrossed products of the disk algebra

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