List questions from banach-spaces

Published on 26 May 2023 - 19:43

98

Views

Show a sum in a Banach space is convergent and bounded

Published on 27 Mar 2026 - 0:50

54

Views

In $l_2^2$, for any two linearly independent extreme points of unit ball $x_p, x_q$, $\|ax_p+bx_q\|= 1\implies |a|\leq 1, |b|\leq 1$

Published on 27 May 2023 - 17:13

40

Views

Weak*-separability of the unit ball of $X’$ and density characters and cardinalities of $X$ and $X’$

Published on 27 Mar 2026 - 21:20

65

Views

Sufficient conditions for series to converge in Banach spaces

Published on 06 Apr 2026 - 7:45

57

Views

When I can truncate a function space to a subspace, in a way that non-negative functions stay non-negative?

Published on 25 Mar 2026 - 12:52

67

Views

Does Riesz-Thorin Theorem hold for Bochner spaces?

Published on 26 Mar 2026 - 4:31

79

Views

Is the sum of a closed unit ball and a closed set itself closed?

Published on 23 Feb 2026 - 4:22

57

Views

Is there an isometric embedding from the Euclidean plane to the sequence space with the $\ell_1$ metric?

Published on 27 Mar 2026 - 15:36

70

Views

For a linear operator $T\in L(X, Y)$, when $T(B(X))=B(Y)$?

Published on 04 Jun 2023 - 16:50

142

Views

Brezis' exercise 6.2.1: If $E$ is reflexive, then $T(B_E)$ is closed in norm topology

Published on 23 Feb 2026 - 6:24

67

Views

Operator whose spectrum is different from the spectrum of its dual

Published on 01 Apr 2026 - 7:17

470

Views

Banach space direct sum

Published on 09 Jun 2023 - 21:25

37

Views

Relations of injective and surjective in adjoint opeerators.

Published on 28 Mar 2026 - 7:37

67

Views

For bounded operators on a Banach space, how far is quasi-compactness from compactness?

Published on 28 Mar 2026 - 6:08

List Question

Polynomial approximation on the closed unit disc

Show a sum in a Banach space is convergent and bounded

In $l_2^2$, for any two linearly independent extreme points of unit ball $x_p, x_q$, $\|ax_p+bx_q\|= 1\implies |a|\leq 1, |b|\leq 1$

Weak*-separability of the unit ball of $X’$ and density characters and cardinalities of $X$ and $X’$

Sufficient conditions for series to converge in Banach spaces

When I can truncate a function space to a subspace, in a way that non-negative functions stay non-negative?

Does Riesz-Thorin Theorem hold for Bochner spaces?

Is the sum of a closed unit ball and a closed set itself closed?

Is there an isometric embedding from the Euclidean plane to the sequence space with the $\ell_1$ metric?

For a linear operator $T\in L(X, Y)$, when $T(B(X))=B(Y)$?

Brezis' exercise 6.2.1: If $E$ is reflexive, then $T(B_E)$ is closed in norm topology

Operator whose spectrum is different from the spectrum of its dual

Banach space direct sum

Relations of injective and surjective in adjoint opeerators.

For bounded operators on a Banach space, how far is quasi-compactness from compactness?

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