List questions from hilbert-spaces

Published on 25 Mar 2026 - 11:12

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Prove that this integral operator is compact

Published on 01 Nov 2014 - 13:17

808

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Square root of a bounded operator in Hilbert space

Published on 02 Nov 2014 - 13:26

489

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Sequence of unitary l.i. vectors such tha the sequence converges weakly to a non-zero vector, but not strongly

Published on 02 Nov 2014 - 18:39

219

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If $V\subset H\subset V^$ is a Gelfand triple, which is the natural inner product on $V^$?

Published on 28 Mar 2026 - 22:55

38

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For continuous Linear functional show $L \notin (C[0,1] , || . ||_2)^* $

Published on 03 Nov 2014 - 21:45

269

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Stone's Theorem Integral: Basic Integral

Published on 03 Nov 2014 - 22:34

6.8k

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Hilbert cube is compact

Published on 02 Apr 2026 - 23:47

1.1k

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Hilbert spaces of holomorphic functions

Published on 30 Mar 2026 - 1:28

479

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WOT convergence to SOT convergence

Published on 29 Mar 2026 - 21:52

67

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If $T = A + iB$, where $A$ and $B$ are self-adjoint operators on a Hilbert space $H$, then this is said to be a Cartesian decomposition of T

Published on 05 Nov 2014 - 13:25

112

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Spectral Measures: Reducibility

Published on 05 Nov 2014 - 13:59

1.3k

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Definition of unitary operators

Published on 05 Nov 2014 - 17:55

125

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Dense convex proper subset of the Hilbert space $l_2$: $\{x|\sum x_i=0\}$

Published on 06 Nov 2014 - 19:35

96

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Prove $Tx=(r_1x_1, r_2x_2, r_3x_3,...)$ is compact, $T:l^2\to l^2$, $r\in l^2$

Published on 26 Mar 2026 - 17:42

List Question

Hypothesis of Riesz's representation theorem

Prove that this integral operator is compact

Square root of a bounded operator in Hilbert space

Sequence of unitary l.i. vectors such tha the sequence converges weakly to a non-zero vector, but not strongly

If $V\subset H\subset V^$ is a Gelfand triple, which is the natural inner product on $V^$?

For continuous Linear functional show $L \notin (C[0,1] , || . ||_2)^* $

Stone's Theorem Integral: Basic Integral

Hilbert cube is compact

Hilbert spaces of holomorphic functions

WOT convergence to SOT convergence

If $T = A + iB$, where $A$ and $B$ are self-adjoint operators on a Hilbert space $H$, then this is said to be a Cartesian decomposition of T

Spectral Measures: Reducibility

Definition of unitary operators

Dense convex proper subset of the Hilbert space $l_2$: $\{x|\sum x_i=0\}$

Prove $Tx=(r_1x_1, r_2x_2, r_3x_3,...)$ is compact, $T:l^2\to l^2$, $r\in l^2$

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