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Mar
3
answered Counterexamples for “every linear map on an infinite dimensional complex vector space has an eigenvalue”
Feb
11
answered $F$ is isomorphic to $\Bbb Z_p$ for some prime number $p$.
Feb
6
awarded  Informed
Feb
5
answered A question about induced $C^\ast$-algebra
Apr
28
comment $X$ second countable locally compact Hausdorff implies $C(X)$ separable?
It makes sense to consider the topology of uniform convergence. However, I think that topology is "too big" to be separable in general, even when $X$ is second countable and LCH.
Apr
28
comment $X$ second countable locally compact Hausdorff implies $C(X)$ separable?
What topology are you considering on $C(X)$? Unless $X$ is compact, the sup norm will not make sense -- you would need to restrict to the set $C_b(X)$ of bounded continuous functions on $X$.
Nov
1
comment Doubts about metrization theorems
To see a proof of the equivalence of the Nagata-Smirnov and Bing characterizations of metrizability, look at Chapter 4, Theorem 18 of Kelley's General Topology.
May
23
comment The image of orthonormal basis under compact operator
What characterizations of compact operators do you know? (Hint: Maybe think about the weak topology on $H$.)
May
18
comment Question about Fredholm operator
They are both complemented: $\ker(A)$ is finite-dimensional, hence complemented, and $\text{im}(A)$ is finite-codimensional, so any algebraic complement is finite-dimensonal, hence closed.
May
16
awarded  Enthusiast
Apr
28
awarded  Supporter
Apr
25
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Apr
25
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Apr
25
answered Compact operator in Hilbert Space