Question

How can we show that $E\:\hat⊗_π F→E\:\hat⊗_ε\:F↪\mathfrak B(E',F')$ is injective iff $E\:\hat⊗_π F→(E'⊗_εF')'↪\mathfrak B(E',F')$ is injective?

score 146 · Answer 1 · 2026-03-17 05:05:18

How can we show that $E\:\hat⊗_π F→E\:\hat⊗_ε\:F↪\mathfrak B(E',F')$ is injective iff $E\:\hat⊗_π F→(E'⊗_εF')'↪\mathfrak B(E',F')$ is injective?

score 1.4k · Answer 2 · 2018-01-24 11:14:22

1.4k

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Is the total variation norm of a measure equal to its norm as a bounded functional?

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score 1.5k · Answer 3 · 2026-03-19 23:51:07

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score 892 · Answer 4 · 2026-03-22 01:25:11

892

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score 128 · Answer 5 · 2026-03-23 10:54:27

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score 50 · Answer 6 · 2026-03-22 12:28:21

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score 81 · Answer 7 · 2026-03-22 20:30:07

81

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To prove x_n is summable under the given norm

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score 135 · Answer 8 · 2026-03-17 17:06:56

If $L∈\mathfrak L(X⊗_πY,E)$, then $\sup_{\left\|x\right\|_X,\:\left\|y\right\|_Y\:≤\:1}\left\|L(x⊗y)\right\|_E=\sup_{π(u)\:≤\:1}\left\|Lu\right\|_E$

score 192 · Answer 9 · 2026-03-17 09:34:52

192

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score 271 · Answer 10 · 2026-03-17 17:02:01

271

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score 91 · Answer 11 · 2026-03-20 10:12:47

91

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score 80 · Answer 12 · 2018-01-30 21:14:34

80

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score 532 · Answer 13 · 2026-03-24 11:52:07

532

Views

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score 138 · Answer 14 · 2018-01-31 16:31:50

$T:X\rightarrow X$ bounded linear operator ($X$ Banach space), $||T||\leq 1$ and $T(x_0)=x_0$, then $x_0\notin \{x-Tx \mid x\in X \}$

score 805 · Answer 15 · 2026-03-16 23:40:54

805

Views

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Published on 16 Mar 2026 - 23:40

List Question

How can we show that $E\:\hat⊗_π F→E\:\hat⊗_ε\:F↪\mathfrak B(E',F')$ is injective iff $E\:\hat⊗_π F→(E'⊗_εF')'↪\mathfrak B(E',F')$ is injective?

Is the total variation norm of a measure equal to its norm as a bounded functional?

Help me understand this proof of Implicit Function Theorem on Banach spaces

The diagonal extraction procedure?

Is it a equivalent semi norm in Campanato space?

X^* closed under pointwise convergence.

To prove x_n is summable under the given norm

If $L∈\mathfrak L(X⊗_πY,E)$, then $\sup_{\left\|x\right\|_X,\:\left\|y\right\|_Y\:≤\:1}\left\|L(x⊗y)\right\|_E=\sup_{π(u)\:≤\:1}\left\|Lu\right\|_E$

Representation of tensors in the projective tensor product

Definition of the approximation property of a Banach space

Banach algebra of functions under composition

Convergence radius $\beta$=sup{|$\lambda$|: $\lambda$ $\in$ $\Bbb K$ , $(\sum_{k=0}^n c_k \lambda^k)_n$ bounded )

Can a linear subspace in Banach space be the union of several other subspaces?

$T:X\rightarrow X$ bounded linear operator ($X$ Banach space), $||T||\leq 1$ and $T(x_0)=x_0$, then $x_0\notin \{x-Tx \mid x\in X \}$

Finding spectrum of given operator

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