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Algebras of operators on Hilbert space, $C^*-$algebras, von Neumann algebras, non-commutative geometry
2
votes
Accepted
Identification of smooth operators with rapidly decreasing matrices
This is, of course, a long story incorporating many strands but I will try to give a quick overview. Firstly, it is, as so often, convenient to skip to a more general framework. In your case, this …
0
votes
What well known results with countability assumptions can be naturally extended to uncountab...
This is a riff on this query, concentrating on aspects of functional analysis and related topics. It is formulated in a conversational manner but is based on the concepts of ind and pro categories wh …
1
vote
An inverse to functional calculus
This is not a complete answer, but too long for a comment. Suppose that you have such a mapping $F$ between the unbounded s.a. operators. First consider its effect on multiples of the identity opera …