List questions from banach-spaces

Published on 24 Apr 2018 - 7:26

37

Views

Result on the power of norm in Banach space?

Published on 24 Apr 2018 - 7:52

153

Views

A set contained in $\varepsilon$-neighborhood of a finite dimensional subspace is totally bounded

Published on 24 Apr 2018 - 9:01

157

Views

The continuity of linear functionals with respect to uniform convergence of entire functions on balls

Published on 24 Mar 2026 - 22:08

76

Views

Integral compact operators

Published on 24 Apr 2018 - 14:22

672

Views

$C_0(X)$ is a subspace of $C_b(X)$

Published on 26 Apr 2018 - 23:34

255

Views

Does there exist an infinite dimensional compact operator on any infinite dimensional Banach space?

Published on 25 Mar 2026 - 7:42

966

Views

Schauder basis that is not Hilbert basis

Published on 25 Mar 2026 - 9:19

76

Views

Proof about the derivative of operators in $L(V,V')$

Published on 25 Mar 2026 - 6:50

42

Views

Show that if $UT=I=VT$ for $T,U,V\in \mathcal B(X)$, then $U=V$.

Published on 30 Apr 2018 - 9:18

915

Views

Every closed subset of a Banach separable space is separable

Published on 30 Apr 2018 - 9:51

29

Views

Why does $(I-T)S_k-I$ equal $I-T^{k+1}-I$?

Published on 01 May 2018 - 15:37

86

Views

When $X$ is Banach, the spectrum of $T$ is either finite or countably infinite.

Published on 25 Mar 2026 - 14:36

221

Views

Let $X$ be Banach space and $X^*$ be its dual space. Let $S\subset X$ be a convex set containing the origin. Prove that $\bar S = S^{**}.$

Published on 25 Mar 2026 - 3:22

317

Views

Dual of l_inf space of bounded sequences in R

Published on 25 Mar 2026 - 3:21

List Question

Example of a Vector space

Result on the power of norm in Banach space?

A set contained in $\varepsilon$-neighborhood of a finite dimensional subspace is totally bounded

The continuity of linear functionals with respect to uniform convergence of entire functions on balls

Integral compact operators

$C_0(X)$ is a subspace of $C_b(X)$

Does there exist an infinite dimensional compact operator on any infinite dimensional Banach space?

Schauder basis that is not Hilbert basis

Proof about the derivative of operators in $L(V,V')$

Show that if $UT=I=VT$ for $T,U,V\in \mathcal B(X)$, then $U=V$.

Every closed subset of a Banach separable space is separable

Why does $(I-T)S_k-I$ equal $I-T^{k+1}-I$?

When $X$ is Banach, the spectrum of $T$ is either finite or countably infinite.

Let $X$ be Banach space and $X^*$ be its dual space. Let $S\subset X$ be a convex set containing the origin. Prove that $\bar S = S^{**}.$

Dual of l_inf space of bounded sequences in R

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