List questions from operator-theory

Published on 08 Apr 2026 - 17:28

98

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Calculate operator norm

Published on 24 Apr 2026 - 18:14

147

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compact operator and bounded operator

Published on 09 Apr 2026 - 1:55

45

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How can we have both $y^\ast \in Y^\ast$ and $y^\ast \in \text{im}(A)^\perp \subset Y$ for an operator $A: X \to Y$?

Published on 24 Apr 2026 - 18:25

923

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Norms of powers of self-adjoint operator

Published on 12 Apr 2026 - 11:35

5.8k

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Hilbert space adjoint vs Banach space adjoint?

Published on 12 Apr 2026 - 20:30

37

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How is $\|T^\ast T\| \ge \sup_{\|x\| = 1} (x, T^\ast Tx) = \sup_{\|x\|=1} \|Tx\|^2 = \|T\|^2$

Published on 16 Apr 2026 - 5:09

588

Views

Square root of compact positive operator

Published on 09 Apr 2026 - 11:00

748

Views

Spectrum of power bounded operator

Published on 09 Apr 2026 - 13:43

2.5k

Views

Why is $\text{dim ker}(T) = 0$ a requirement for invertibility of a finite dimensional operator, but not for an infinite dimensional operator?

Published on 12 Apr 2026 - 8:51

269

Views

Blaschke product is proper holomorphic map

Published on 13 Apr 2026 - 1:09

893

Views

Can't find elements in the kernel of the right shift operator $S[(x_1, x_2, \dots)] = (0, x_1, x_2, \dots)$?

Published on 17 Apr 2026 - 11:45

64

Views

Existence as a linear and bounded operator and nonexpansive

Published on 12 Apr 2026 - 13:29

165

Views

Polar decomposition: analogy between unit circle and partial isometry

Published on 10 Apr 2026 - 22:29

4.7k

Views

Spectrum of the derivative operator

Published on 10 Apr 2026 - 0:23

List Question

proof: Hilbert Schmidt operator is compact

Calculate operator norm

compact operator and bounded operator

How can we have both $y^\ast \in Y^\ast$ and $y^\ast \in \text{im}(A)^\perp \subset Y$ for an operator $A: X \to Y$?

Norms of powers of self-adjoint operator

Hilbert space adjoint vs Banach space adjoint?

How is $\|T^\ast T\| \ge \sup_{\|x\| = 1} (x, T^\ast Tx) = \sup_{\|x\|=1} \|Tx\|^2 = \|T\|^2$

Square root of compact positive operator

Spectrum of power bounded operator

Why is $\text{dim ker}(T) = 0$ a requirement for invertibility of a finite dimensional operator, but not for an infinite dimensional operator?

Blaschke product is proper holomorphic map

Can't find elements in the kernel of the right shift operator $S[(x_1, x_2, \dots)] = (0, x_1, x_2, \dots)$?

Existence as a linear and bounded operator and nonexpansive

Polar decomposition: analogy between unit circle and partial isometry

Spectrum of the derivative operator

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