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Miron Shpigel

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Papers by Miron Shpigel

Research paper thumbnail of The Ideal Structure of Some Analytic Crossed Products

We study the ideal structure of a class of some analytic crossed products. For an r-discrete, pri... more We study the ideal structure of a class of some analytic crossed products. For an r-discrete, principal, minimal groupoid G, we consider the analytic crossed product C(G; ) Z+ ,w hereis given by a cocycle c. We show that the maximal ideal space M of C(G; ) Z+ depends on the asymptotic range of c, R1(c); that is, M is

Research paper thumbnail of Isometric Dilations of Non-Commuting Finite Rank <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span>-Tuples

Canadian Journal of Mathematics, 2001

A contractive n-tuple A = (A1,…,An ) has a minimal joint isometric dilation S = (S 1,…,S n) where... more A contractive n-tuple A = (A1,…,An ) has a minimal joint isometric dilation S = (S 1,…,S n) where the Si ’s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When A acts on a finite dimensional space, the wot-closed nonself-adjoint algebra generated by S is completely described in terms of the properties of A. This provides complete unitary invariants for the corresponding representations. In addition, we show that the algebra is always hyper-reflexive. In the last section, we describe similarity invariants. In particular, an n-tuple B of d × d matrices is similar to an irreducible n-tuple A if and only if a certain finite set of polynomials vanish on B.

Research paper thumbnail of The Ideal Structure of Some Analytic Crossed Products

We study the ideal structure of a class of some analytic crossed products. For an r-discrete, pri... more We study the ideal structure of a class of some analytic crossed products. For an r-discrete, principal, minimal groupoid G, we consider the analytic crossed product C(G; ) Z+ ,w hereis given by a cocycle c. We show that the maximal ideal space M of C(G; ) Z+ depends on the asymptotic range of c, R1(c); that is, M is

Research paper thumbnail of Isometric Dilations of Non-Commuting Finite Rank <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">n</span></span></span></span>-Tuples

Canadian Journal of Mathematics, 2001

A contractive n-tuple A = (A1,…,An ) has a minimal joint isometric dilation S = (S 1,…,S n) where... more A contractive n-tuple A = (A1,…,An ) has a minimal joint isometric dilation S = (S 1,…,S n) where the Si ’s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When A acts on a finite dimensional space, the wot-closed nonself-adjoint algebra generated by S is completely described in terms of the properties of A. This provides complete unitary invariants for the corresponding representations. In addition, we show that the algebra is always hyper-reflexive. In the last section, we describe similarity invariants. In particular, an n-tuple B of d × d matrices is similar to an irreducible n-tuple A if and only if a certain finite set of polynomials vanish on B.

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