Question

If $P$ is a projection and $T$ is positive operator such that $P\leq T$, then why $P(H)\subset\sqrt{T}(H)$?

score 145 · Answer 1 · 2026-03-25 17:33:53

145

Views

If $P$ is a projection and $T$ is positive operator such that $P\leq T$, then why $P(H)\subset\sqrt{T}(H)$?

Published on 25 Mar 2026 - 17:33

score 604 · Answer 2 · 2026-03-27 10:09:55

604

Views

On the existence of the adjoint of a densely defined unbounded operator

Published on 27 Mar 2026 - 10:09

score 19 · Answer 3 · 2026-04-09 14:54:25

19

Views

Markov Chains on $\mathbb{C}^N$ are all the positive unital maps on $\mathbb{C}^N$

Published on 09 Apr 2026 - 14:54

score 33 · Answer 4 · 2026-03-31 03:26:53

33

Views

Algebra product on the commutative $C^*$-algebra $\mathbb{C}^N$

Published on 31 Mar 2026 - 3:26

score 39 · Answer 5 · 2026-04-12 04:56:29

39

Views

Separable Operators in a Hilbert Space.

Published on 12 Apr 2026 - 4:56

score 31 · Answer 6 · 2026-03-26 04:53:26

31

Views

If $U$ is a linear isometry on $H$, then $\frac1n\left\|(1-U^n)x\right\|_H\xrightarrow{n\to\infty}0$

Published on 26 Mar 2026 - 4:53

score 126 · Answer 7 · 2026-04-08 23:07:44

126

Views

Under what conditions can an operator be moved under the integral

Published on 08 Apr 2026 - 23:07

score 220 · Answer 8 · 2026-03-25 17:29:49

220

Views

inequality for positive contraction operator

Published on 25 Mar 2026 - 17:29

score 248 · Answer 9 · 2026-04-07 14:43:59

248

Views

The range of the Multiplication operator $R(T_f)=L^2(\mu)$ iff $\exists \epsilon > 0$ st. $|f|>\epsilon $ a.e.

Published on 07 Apr 2026 - 14:43

score 147 · Answer 10 · 2026-03-27 03:43:19

147

Views

Why is this representation of $C^*\!$-algebras irreducible?

Published on 27 Mar 2026 - 3:43

score 331 · Answer 11 · 2026-03-27 07:49:17

331

Views

What is adjoint of extended right shift operator on a Hilbert space?

Published on 27 Mar 2026 - 7:49

score 155 · Answer 12 · 2026-04-13 04:50:40

155

Views

A linear operator $A:X \rightarrow Y$, where $Y$ is Banach, is compact if and only if the image of the unit sphere is sequentially compact

Published on 13 Apr 2026 - 4:50

score 319 · Answer 13 · 2026-03-26 06:21:31

319

Views

If every isometry on a Hilbert space is unitary, then $H$ is finite dimensional.

Published on 26 Mar 2026 - 6:21

score 27 · Answer 14 · 2026-04-11 05:33:43

27

Views

$C^*$- systems with positive maps

Published on 11 Apr 2026 - 5:33

score 438 · Answer 15 · 2026-03-25 17:31:29

438

Views

Hilbert space self adjoint and idempotent

Published on 25 Mar 2026 - 17:31

List Question

If $P$ is a projection and $T$ is positive operator such that $P\leq T$, then why $P(H)\subset\sqrt{T}(H)$?

On the existence of the adjoint of a densely defined unbounded operator

Markov Chains on $\mathbb{C}^N$ are all the positive unital maps on $\mathbb{C}^N$

Algebra product on the commutative $C^*$-algebra $\mathbb{C}^N$

Separable Operators in a Hilbert Space.

If $U$ is a linear isometry on $H$, then $\frac1n\left\|(1-U^n)x\right\|_H\xrightarrow{n\to\infty}0$

Under what conditions can an operator be moved under the integral

inequality for positive contraction operator

The range of the Multiplication operator $R(T_f)=L^2(\mu)$ iff $\exists \epsilon > 0$ st. $|f|>\epsilon $ a.e.

Why is this representation of $C^*\!$-algebras irreducible?

What is adjoint of extended right shift operator on a Hilbert space?

A linear operator $A:X \rightarrow Y$, where $Y$ is Banach, is compact if and only if the image of the unit sphere is sequentially compact

If every isometry on a Hilbert space is unitary, then $H$ is finite dimensional.

$C^*$- systems with positive maps

Hilbert space self adjoint and idempotent

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