Question

Is $\mbox{Im}(T_0)$ a closed subspace of $\overline{\mbox{Im}(T)}$ with respect to $\|\cdot\|$?

score 49 · Answer 1 · 2026-03-25 04:43:48

49

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Is $\mbox{Im}(T_0)$ a closed subspace of $\overline{\mbox{Im}(T)}$ with respect to $\|\cdot\|$?

Published on 25 Mar 2026 - 4:43

score 157 · Answer 2 · 2026-03-25 03:07:51

157

Views

Convergence and non-convergence of operators on a hilbert space

Published on 25 Mar 2026 - 3:07

score 78 · Answer 3 · 2026-03-25 01:27:57

78

Views

Show that $I-A$ is invertible iff $a_{k,k} \neq 1$ for all $k$

Published on 25 Mar 2026 - 1:27

score 68 · Answer 4 · 2026-03-26 12:07:04

68

Views

Confused about some norms with a variety of subscripts

Published on 26 Mar 2026 - 12:07

score 53 · Answer 5 · 2018-01-30 20:17:00

53

Views

Why Do We Need The Requirement of "Ordered by Inclusion" in this Theorem?

Published on 30 Jan 2018 - 20:17

score 300 · Answer 6 · 2026-03-23 23:15:00

300

Views

Examples of unbounded approximate units in $C^*$-algebras

Published on 23 Mar 2026 - 23:15

score 92 · Answer 7 · 2026-03-25 15:39:33

92

Views

Banach algebra of functions under composition

Published on 25 Mar 2026 - 15:39

score 81 · Answer 8 · 2026-03-25 06:09:38

81

Views

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

Published on 25 Mar 2026 - 6:09

score 63 · Answer 9 · 2018-01-30 21:43:18

63

Views

Is operator A compact?

Published on 30 Jan 2018 - 21:43

score 532 · Answer 10 · 2026-03-24 11:52:07

532

Views

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

Published on 24 Mar 2026 - 11:52

score 806 · Answer 11 · 2026-03-24 23:41:07

806

Views

Calculate convolution (integral)

Published on 24 Mar 2026 - 23:41

score 43 · Answer 12 · 2018-01-31 04:20:30

43

Views

vector space with a metric

Published on 31 Jan 2018 - 4:20

score 642 · Answer 13 · 2026-03-25 19:07:18

642

Views

If $Y$ is a compact subset of $X$, and $Z\subset Y$, then $Z$ is compact if and only if $Z$ is closed.

Published on 25 Mar 2026 - 19:07

score 245 · Answer 14 · 2026-03-25 19:07:08

245

Views

If $Y_1,...,Y_n$ are a finite collection of compact subsets of $X$, then their union $Y_1\cup....\cup Y_n$ are also compact.

Published on 25 Mar 2026 - 19:07

score 139 · Answer 15 · 2026-03-25 06:13:28

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

List Question

Is $\mbox{Im}(T_0)$ a closed subspace of $\overline{\mbox{Im}(T)}$ with respect to $\|\cdot\|$?

Convergence and non-convergence of operators on a hilbert space

Show that $I-A$ is invertible iff $a_{k,k} \neq 1$ for all $k$

Confused about some norms with a variety of subscripts

Why Do We Need The Requirement of "Ordered by Inclusion" in this Theorem?

Examples of unbounded approximate units in $C^*$-algebras

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 )

Is operator A compact?

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

Calculate convolution (integral)

vector space with a metric

If $Y$ is a compact subset of $X$, and $Z\subset Y$, then $Z$ is compact if and only if $Z$ is closed.

If $Y_1,...,Y_n$ are a finite collection of compact subsets of $X$, then their union $Y_1\cup....\cup Y_n$ are also compact.

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

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