List questions from hilbert-spaces

Published on 03 Apr 2026 - 8:46

154

Views

Basis of $H^1(\Omega)$ which is orthonormal wrt. $L^2(\partial\Omega)$ inner product?

Published on 26 Mar 2026 - 17:46

80

Views

What is the 'largest' space of integrable functions which is also a Hilbert space?

Published on 02 Apr 2026 - 17:43

76

Views

Show that a subspace is closed in Hilbert space $H$

Published on 29 Mar 2026 - 4:47

29

Views

On the polar representation of an inner product.

Published on 01 Apr 2026 - 21:02

107

Views

Construct a bounded linear operator $S$ on $H$ such that $\sigma(S) = A$

Published on 28 Mar 2026 - 16:59

166

Views

Construct a unitary operator U on H with prescribed spectrum

Published on 28 Mar 2026 - 15:26

4k

Views

What is the orthogonal of an intersection?

Published on 28 Mar 2026 - 21:26

239

Views

The Spectral Radius of a Product of Two Hilbert-Space Operators

Published on 23 Dec 2014 - 2:04

398

Views

Determining the orthogonal complement of $\{1 \}^\perp$ in $L^2[0,1]$

Published on 02 Apr 2026 - 17:42

675

Views

On the intuition behind the projection theorem.

Published on 01 Apr 2026 - 22:34

2.5k

Views

The inner product of the Cartesian Product space

Published on 25 Dec 2014 - 23:07

1.8k

Views

$L_2$ norm and RHKS norm in Hilbert spaces $\mathcal{H}$

Published on 26 Dec 2014 - 2:56

12.4k

Views

What is the definition of closed subspace?

Published on 01 Apr 2026 - 22:36

87

Views

Why $\|f\|_2^2$ can be written as $\int |f(x)|^2 p(x)dx$?

Published on 27 Dec 2014 - 13:40

List Question

Approximate the unit ball in an infinite-dimensional Hilbert space, by compact sets?

Basis of $H^1(\Omega)$ which is orthonormal wrt. $L^2(\partial\Omega)$ inner product?

What is the 'largest' space of integrable functions which is also a Hilbert space?

Show that a subspace is closed in Hilbert space $H$

On the polar representation of an inner product.

Construct a bounded linear operator $S$ on $H$ such that $\sigma(S) = A$

Construct a unitary operator U on H with prescribed spectrum

What is the orthogonal of an intersection?

The Spectral Radius of a Product of Two Hilbert-Space Operators

Determining the orthogonal complement of $\{1 \}^\perp$ in $L^2[0,1]$

On the intuition behind the projection theorem.

The inner product of the Cartesian Product space

$L_2$ norm and RHKS norm in Hilbert spaces $\mathcal{H}$

What is the definition of closed subspace?

Why $\|f\|_2^2$ can be written as $\int |f(x)|^2 p(x)dx$?

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