"Non UBC"@en .
"DSpace"@en .
"Phillips, N. Christopher"@en .
"2014-08-07T00:11:00Z"@en .
"2013-04-24"@en .
"Graph algebras have been intensively studied in the C* and purely algebraic contexts. We propose another context: Banach algebras of operators on Lp spaces. We report on results on the analogs in this context of Cuntz algebras and UHF algebras. (The analogs of UHF algebras are needed for the proofs of some of the results on the analogs of Cuntz algebras.)\n\nFor p \u00E2\u0088\u0088 [1, \u00E2\u0088\u009E) and d \u00E2\u0088\u0088 {2, 3, . . .}, we identify a \u00E2\u0080\u009Cgood\u00E2\u0080\u009D analog Odp of the Cuntz algebra Od which acts\non spaces of the form Lp(X,\u00CE\u00BC). We prove uniqueness and simplicity of Odp. Unlike the C* case, these two\nresults seem to be independent, and our proofs of the two results are entirely unrelated. We further prove\nthat Odp is purely infinite and amenable as a Banach algebra, and we compute its topological K-theory,\ngetting the expected answer. We prove that for d1,d2 \u00E2\u0088\u0088 {2,3,...} and for p1 \u00E2\u0089\u00A0 p2, there is no nonzero\ncontinuous homomorphism from Op1 to Op2. We leave a number of problems open. In particular, we do pd1d2pp p\nnot know whether the L spatial tensor product O2 \u00E2\u008A\u0097p O2 is isomorphic to O2 for p \u00CC\u00B8= 2.\n\nWe prove that the \u00E2\u0080\u009Cgood\u00E2\u0080\u009D Lp analogs of UHF algebras are unique in a suitable sense, simple, amenable, have a unique continuous trace, and have the expected K-theory. We show that for each p and each supernatural number, there are uncountably many mutually nonisomorphic Lp UHF algebras with the same supernatural number and having all the properties given above except uniqueness and amenability. \n\nThis talk will be primarily a survey, but will explain some of the key ideas."@en .
"https://circle.library.ubc.ca/rest/handle/2429/49469?expand=metadata"@en .
"62 minutes"@en .
"video/mp4"@en .
""@en .
"Author affiliation: University of Oregon"@en .
"10.14288/1.0043523"@en .
"eng"@en .
"Unreviewed"@en .
"Vancouver : University of British Columbia Library"@en .
"Banff International Research Station for Mathematical Innovation and Discovery"@en .
"Attribution-NonCommercial-NoDerivs 2.5 Canada"@en .
"http://creativecommons.org/licenses/by-nc-nd/2.5/ca/"@en .
"Faculty"@en .
"BIRS Workshop Lecture Videos (Banff, Alta)"@en .
"Mathematics"@en .
"Functional analysis"@en .
"Associative rings and algebras"@en .
"Operator theory/algebras"@en .
"Analogs of Cuntz algebras on Lp spaces"@en .
"Moving Image"@en .
"http://hdl.handle.net/2429/49469"@en .