Question

The Banach algebra of bounded operators on a separable Hilbert space has a countable dense subset

score 100 · Answer 1 · 2026-03-25 09:26:21

100

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The Banach algebra of bounded operators on a separable Hilbert space has a countable dense subset

Published on 25 Mar 2026 - 9:26

score 363 · Answer 2 · 2026-03-25 11:21:47

363

Views

if $Y$ is eigenspace to an eigenvalue $\lambda$ of an operator $T,$ and if $T_1$ is restriction of $T$ to $Y$. find spectrum of $\sigma(T_1)$

Published on 25 Mar 2026 - 11:21

score 1k · Answer 3 · 2018-03-13 16:53:49

1k

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Show that $(X,\|\cdot\|)$ is complete if and only if $(X,|\!|\!|\cdot|\!|\!|)$ is complete when both norms are equivalent.

Published on 13 Mar 2018 - 16:53

score 311 · Answer 4 · 2026-03-23 01:59:52

311

Views

comparing two Sobolev spaces:$W_0^{s,p}(\Omega)$ and $\overline{ C_c^{\infty}(\Omega)}^{~~W^{s,p}(\Bbb R^d)}$

Published on 23 Mar 2026 - 1:59

score 332 · Answer 5 · 2026-03-25 06:03:26

332

Views

$L^p$ Banach $ \implies L^2$ Hilbert by Jordan-von Neumann Theorem?

Published on 25 Mar 2026 - 6:03

score 757 · Answer 6 · 2018-03-14 22:20:10

757

Views

Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space

Published on 14 Mar 2018 - 22:20

score 562 · Answer 7 · 2026-03-25 06:01:38

562

Views

$l_p$ norm and Banach

Published on 25 Mar 2026 - 6:01

score 272 · Answer 8 · 2026-03-25 12:09:06

272

Views

Embedding of weighted Holder space into $L^p$

Published on 25 Mar 2026 - 12:09

score 870 · Answer 9 · 2026-03-25 07:44:42

870

Views

A sequence $\{x_n\}$ in a Banach space converging weakly to $x \in X$ such that $||x_n|| \le ||x||, \forall n \in \mathbb N$

Published on 25 Mar 2026 - 7:44

score 74 · Answer 10 · 2018-03-15 20:36:09

74

Views

Verify the well-defined in the proof of Hahn Banach Theorem.

Published on 15 Mar 2018 - 20:36

score 554 · Answer 11 · 2026-03-25 00:07:42

554

Views

Show that a closed self-adjoint subalgebra of a $C^$-algebra is also a $C^$-algebra.

Published on 25 Mar 2026 - 0:07

score 125 · Answer 12 · 2026-03-19 23:33:53

125

Views

Arzela-Ascoli argument on a partition

Published on 19 Mar 2026 - 23:33

score 101 · Answer 13 · 2026-03-25 01:27:00

101

Views

Approximating the limit of a Cauchy sequence in a Banach space

Published on 25 Mar 2026 - 1:27

score 67 · Answer 14 · 2026-03-25 10:52:59

67

Views

Weak convergence in Banach spaces $C^{k}[0,1]$

Published on 25 Mar 2026 - 10:52

score 322 · Answer 15 · 2026-03-24 23:52:51

322

Views

Infinity norm quotient

Published on 24 Mar 2026 - 23:52

List Question

The Banach algebra of bounded operators on a separable Hilbert space has a countable dense subset

if $Y$ is eigenspace to an eigenvalue $\lambda$ of an operator $T,$ and if $T_1$ is restriction of $T$ to $Y$. find spectrum of $\sigma(T_1)$

Show that $(X,\|\cdot\|)$ is complete if and only if $(X,|\!|\!|\cdot|\!|\!|)$ is complete when both norms are equivalent.

comparing two Sobolev spaces:$W_0^{s,p}(\Omega)$ and $\overline{ C_c^{\infty}(\Omega)}^{~~W^{s,p}(\Bbb R^d)}$

$L^p$ Banach $ \implies L^2$ Hilbert by Jordan-von Neumann Theorem?

Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space

$l_p$ norm and Banach

Embedding of weighted Holder space into $L^p$

A sequence $\{x_n\}$ in a Banach space converging weakly to $x \in X$ such that $||x_n|| \le ||x||, \forall n \in \mathbb N$

Verify the well-defined in the proof of Hahn Banach Theorem.

Show that a closed self-adjoint subalgebra of a $C^$-algebra is also a $C^$-algebra.

Arzela-Ascoli argument on a partition

Approximating the limit of a Cauchy sequence in a Banach space

Weak convergence in Banach spaces $C^{k}[0,1]$

Infinity norm quotient

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