Question

How is obtained the following representation for the heat semigroup?

score 756 · Answer 1 · 2026-03-26 03:11:40

756

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How is obtained the following representation for the heat semigroup?

Published on 26 Mar 2026 - 3:11

score 234 · Answer 2 · 2016-10-13 03:32:58

234

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Norm of the resolvent of the right shift operator on $\ell^2$

Published on 13 Oct 2016 - 3:32

score 92 · Answer 3 · 2016-10-13 12:46:33

92

Views

Uniformly Bounded invertible linear operators have their inverses with norms uniformly bounded

Published on 13 Oct 2016 - 12:46

score 470 · Answer 4 · 2016-10-13 13:13:05

470

Views

Eigenvalues of bounded linear operator

Published on 13 Oct 2016 - 13:13

score 274 · Answer 5 · 2026-03-27 14:54:04

274

Views

Non-empty point spectrum of an operator which commutes with a non-quasinilpotent compact operator

Published on 27 Mar 2026 - 14:54

score 103 · Answer 6 · 2026-03-27 22:31:00

103

Views

Banach algebra: for $\lambda$ not in the spectrum of $a$, $\Vert (\lambda - a)^{-1} \Vert \ge 1/\text{dist}(\lambda, \sigma(a))$

Published on 27 Mar 2026 - 22:31

score 359 · Answer 7 · 2016-10-22 14:47:02

359

Views

What Mathematical Object Does a "Functional Calculus" Correspond to Precisely?

Published on 22 Oct 2016 - 14:47

score 80 · Answer 8 · 2016-10-23 15:43:02

80

Views

Given a spectrum, how to deduce the space and the operator?

Published on 23 Oct 2016 - 15:43

score 137 · Answer 9 · 2016-10-23 23:12:00

137

Views

Infimum of spectrum differentiable if resolvent norm-differentiable?

Published on 23 Oct 2016 - 23:12

score 173 · Answer 10 · 2016-10-27 00:29:41

173

Views

Do "close" operators have "close" spectra?

Published on 27 Oct 2016 - 0:29

score 128 · Answer 11 · 2026-03-26 19:37:49

128

Views

Perturbation of Normal Operator

Published on 26 Mar 2026 - 19:37

score 57 · Answer 12 · 2026-03-26 02:58:19

57

Views

Test for equivalence of eigenvalues that are numerically distinct?

Published on 26 Mar 2026 - 2:58

score 30 · Answer 13 · 2026-03-27 14:56:48

30

Views

$\mathscr{N}(S^{n_{0}})=\mathscr{N}(S^{n_{0}+1})$ for some $n_{0}$ $\implies\mathscr{N}(S^{n_{0}})=\mathscr{N}(S^{n_{0}+k})$ for all $k\in\mathbb{N}$.

Published on 27 Mar 2026 - 14:56

score 39 · Answer 14 · 2016-11-01 06:36:09

39

Views

$E^{A\oplus B}(t,\infty) =E^{A}(t,\infty)+E^{B}(t,\infty) $?

Published on 01 Nov 2016 - 6:36

score 33 · Answer 15 · 2016-11-02 03:59:16

33

Views

Whether the spectral projection $E^{T}(0,\frac1n)\downarrow 0$ as $n\rightarrow \infty$ in the strong operator topology?

Published on 02 Nov 2016 - 3:59

List Question

How is obtained the following representation for the heat semigroup?

Norm of the resolvent of the right shift operator on $\ell^2$

Uniformly Bounded invertible linear operators have their inverses with norms uniformly bounded

Eigenvalues of bounded linear operator

Non-empty point spectrum of an operator which commutes with a non-quasinilpotent compact operator

Banach algebra: for $\lambda$ not in the spectrum of $a$, $\Vert (\lambda - a)^{-1} \Vert \ge 1/\text{dist}(\lambda, \sigma(a))$

What Mathematical Object Does a "Functional Calculus" Correspond to Precisely?

Given a spectrum, how to deduce the space and the operator?

Infimum of spectrum differentiable if resolvent norm-differentiable?

Do "close" operators have "close" spectra?

Perturbation of Normal Operator

Test for equivalence of eigenvalues that are numerically distinct?

$\mathscr{N}(S^{n_{0}})=\mathscr{N}(S^{n_{0}+1})$ for some $n_{0}$ $\implies\mathscr{N}(S^{n_{0}})=\mathscr{N}(S^{n_{0}+k})$ for all $k\in\mathbb{N}$.

$E^{A\oplus B}(t,\infty) =E^{A}(t,\infty)+E^{B}(t,\infty) $?

Whether the spectral projection $E^{T}(0,\frac1n)\downarrow 0$ as $n\rightarrow \infty$ in the strong operator topology?

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