List questions from operator-theory

Published on 25 Mar 2026 - 17:21

160

Views

How can we use Hahn-Banach Theorem to prove a functional is linear and bounded?

Published on 25 Mar 2026 - 17:25

48

Views

Right half-plane in resolvent set of $B$. Why is $B$ invertible?

Published on 26 Mar 2026 - 2:55

52

Views

Can a non-invertible isometry on $L^p$ space have index zero?

Published on 27 Mar 2026 - 8:42

490

Views

Separable Hilbert space implies countable number of eigenvalues

Published on 26 Mar 2026 - 2:53

104

Views

Under what conditions does $A \succeq B \succeq 0$ imply $A^2 \succeq B^2$?

Published on 25 Mar 2026 - 6:12

375

Views

In what way is convergence in operator norm 'better' than other forms of convergence?

Published on 25 Mar 2026 - 23:10

1.1k

Views

Is a linear operator continuous if its kernel is closed?

Published on 29 Sep 2018 - 15:29

110

Views

Sufficient condition for element to be close to an invertible in Rordam's Simple C$^{*}$-algebras paper

Published on 26 Mar 2026 - 1:11

112

Views

Proving a property by using the spectral theorem

Published on 30 Sep 2018 - 12:17

78

Views

Choosing eigenvectors and eigenvalues continuously

Published on 26 Mar 2026 - 2:51

496

Views

Irreducible *-representations of $M_n(\mathbb{C})$

Published on 26 Mar 2026 - 1:09

490

Views

Is the extension of $*$ homomorphism unique?

Published on 26 Mar 2026 - 1:14

330

Views

Representation of ordinary differential operators in terms of a given regular operator

Published on 25 Mar 2026 - 7:53

45

Views

Spectrum of off diagonal matrices of operators?

Published on 05 Oct 2018 - 8:38

List Question

To show an element in the sprectum of a matrix $M$ is negative in the spectrum of $-M$

How can we use Hahn-Banach Theorem to prove a functional is linear and bounded?

Right half-plane in resolvent set of $B$. Why is $B$ invertible?

Can a non-invertible isometry on $L^p$ space have index zero?

Separable Hilbert space implies countable number of eigenvalues

Under what conditions does $A \succeq B \succeq 0$ imply $A^2 \succeq B^2$?

In what way is convergence in operator norm 'better' than other forms of convergence?

Is a linear operator continuous if its kernel is closed?

Sufficient condition for element to be close to an invertible in Rordam's Simple C$^{*}$-algebras paper

Proving a property by using the spectral theorem

Choosing eigenvectors and eigenvalues continuously

Irreducible *-representations of $M_n(\mathbb{C})$

Is the extension of $*$ homomorphism unique?

Representation of ordinary differential operators in terms of a given regular operator

Spectrum of off diagonal matrices of operators?

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