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Results tagged with fa.functional-analysis
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user 8435
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
2
votes
1
answer
121
views
Approximation of an Operator
Suppose that $A$ is an bounded linear operator on a Hilbert space such that $\left\|A\right\| \leq 1$. Can we approximate $A$ by an operator $\tilde{A}$ such that $\tilde{A} = \sum_{n=1}^N \alpha_n R …
- 3,699
11
votes
1
answer
962
views
Applications of the "almost commuting" theorem of H. Lin
H. Lin proved that "almost commuting" hermitian matrices are "nearly commuting." To be more precise, Lin showed that given $\epsilon > 0$ there exists a $\delta > 0$ such that if $A, B \in M_N$ are s …
- 3,699
1
vote
Understanding/Mastering Analysis in Topology, necessary?
I was working with some fellow grad students (studying algebraic topology) a few years ago and they were having trouble computing some integrals. This was not unusual, but then they asked me if one e …
- 3,699
3
votes
Are almost commuting hermitian matrices close to commuting matrices (in the 2-norm)?
As part of my dissertation, "Almost Commuting Operators on von Neumann Algebras,"
I have extended Glebsky's result to the normalized Schatten class for $1 \leq p < \infty$. Moreover, for $p=2$ we re …
- 3,699