List questions from operator-theory

Published on 03 Nov 2018 - 14:21

1.1k

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Prove that the right shift operator $S(x_1,x_2, \dots) = (0,x_1,x_2,\dots)$ is bounded.

Published on 03 Nov 2018 - 15:07

6.1k

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Every linear operator $T:X \to Y$ on a finite-dimensional normed space is bounded

Published on 03 Nov 2018 - 16:09

103

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Kernel of an operator

Published on 25 Mar 2026 - 12:52

87

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Limit of an operator and eigenvalues

Published on 25 Mar 2026 - 16:06

732

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Neumann Series Invertibility

Published on 27 Mar 2026 - 14:57

157

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Domain issues with Weyl quantization

Published on 27 Mar 2026 - 4:14

147

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Spectrum and Convergence of an operator

Published on 22 Mar 2026 - 5:20

37

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Self-adjoint operator or not?

Published on 26 Mar 2026 - 7:37

316

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If $X^{(n)},X$ are càdlàg and $X^{(n)}\to X$ in distribution, do the corresponding transition semigroups strongly converge?

Published on 25 Mar 2026 - 4:43

57

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Prove that $\left|\left|I-\frac{ss^t}{s^ts}\right|\right|=1$

Published on 31 Mar 2026 - 5:03

67

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Functions satisfying $\int_0^1\cos(\pi x)f(x) = \int_0^1\sin(\pi x )f(x) = 0$

Published on 05 Nov 2018 - 5:58

263

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A unitary operator commuting with a projection

Published on 05 Nov 2018 - 10:01

205

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Operator norm convergence in functional calculus

Published on 22 Mar 2026 - 16:58

46

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Invertitbility of operator in functional calculus

Published on 23 Feb 2026 - 1:18

List Question

Show that $Tf(x) = g(x)f(x), \; \forall x\in [a,b]$ is a bounded linear operator $T \in B(X)$ .

Prove that the right shift operator $S(x_1,x_2, \dots) = (0,x_1,x_2,\dots)$ is bounded.

Every linear operator $T:X \to Y$ on a finite-dimensional normed space is bounded

Kernel of an operator

Limit of an operator and eigenvalues

Neumann Series Invertibility

Domain issues with Weyl quantization

Spectrum and Convergence of an operator

Self-adjoint operator or not?

If $X^{(n)},X$ are càdlàg and $X^{(n)}\to X$ in distribution, do the corresponding transition semigroups strongly converge?

Prove that $\left|\left|I-\frac{ss^t}{s^ts}\right|\right|=1$

Functions satisfying $\int_0^1\cos(\pi x)f(x) = \int_0^1\sin(\pi x )f(x) = 0$

A unitary operator commuting with a projection

Operator norm convergence in functional calculus

Invertitbility of operator in functional calculus

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