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DTSTART;TZID=America/Los_Angeles:20220922T160000
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CREATED:20220918T041430Z
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UID:2930-1663862400-1663866000@colleges.claremont.edu
SUMMARY:Frobenius-Rieffel norms on matrix algebras (Konrad Aguilar\, Pomona)
DESCRIPTION:Noncommutative metric geometry is the study of certain noncommuative algebras in the context of metric geometry. For instance\, the Lipschitz constant (which measures the maximum slope obtained by a real-valued continuous function on a metric space (allowed to be infinite)) is a vital tool in metric geometry\, and a main feature of noncommutative metric geometry is the introduction of a noncommutative notion of the Lipschitz constant\, called an L-seminorm\, due to M.A. Rieffel. The purpose of our work is to introduce suitable L-seminorms on matrix algebras. To accomplish this\, we used norms introduced by Rieffel on certain unital C*-algebras built from conditional expectations onto unital C*-subalgebras. We begin by showing that these norms generalize the Frobenius norm on matrix algebras\, and we provide explicit formulas for certain conditional expectations onto unital C*-subalgebras of finite-dimensional C*-algebras. This allows us to compare these norms to the unique C*-norm (the operator 2-norm)\, by finding explicit equivalence constants. (This is joint work with Stephan R. Garcia and Elena Kim (’21)\, arxiv: 2112.13164).
URL:https://colleges.claremont.edu/ccms/event/frobenius-rieffel-norms-on-matrix-algebras-konrad-aguilar-pomona/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
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DTSTART;TZID=America/Los_Angeles:20220908T160000
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CREATED:20220905T060933Z
LAST-MODIFIED:20230816T041748Z
UID:2824-1662652800-1662656400@colleges.claremont.edu
SUMMARY:Factorization theorems of Backward Shifts and Nuclear Maps (Asuman Aksoy\, CMC)
DESCRIPTION:The theory of compact linear operators between Banach spaces has a classical core and is familiar to many. Perhaps lesser known is the factorization of compact maps through a closed subspace of \(c_0\) [2]. This factorization theorem has a number of important connections and consequences analogous to how the ideals of continuous linear operators factoring compactly through \(\ell^p\)-spaces \((1\leq p < \infty)\) (see [1] and the references therein). In this talk\, even though hypercyclic operators are not compact\, we consider operator ideals generated by hypercyclic backward weighted shifts and examine their factorization properties. (Joint work with Yunied Puig)\n\n\n\nFourie\, Jan H. Injective and surjective hulls of classical \(p\)-compact operators with application to unconditionally \(p\)-compact operators. Studia Math.  240  (2018)\, no. 2\, 147–159. MR3720927\nTerzioğlu\, T. A characterization of compact linear mappings. Arch. Math. (Basel) 22 (1971)\, 76–78. MR0291865
URL:https://colleges.claremont.edu/ccms/event/factorization-theorems-of-backward-shifts-and-nuclear-maps-asuman-aksoy-cmc/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
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