List questions from hilbert-spaces

Published on 30 Mar 2026 - 17:04

71

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Find $\|x\|$ when $\langle x,e_k \rangle=1/2^k$

Published on 26 Mar 2026 - 17:43

515

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Is the point spectrum always countable?

Published on 28 Mar 2026 - 23:57

376

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Normal plus compact is Fredholm with index 0

Published on 16 Oct 2019 - 9:19

442

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How is the quotient space H/K is isomorphic to the orthogonal complement of K?

Published on 25 Mar 2026 - 11:03

38

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Do the transpose operator and the adjoint operator have same ranges and kernels?

Published on 26 Mar 2026 - 0:59

29

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Relation between two subspaces

Published on 16 Oct 2019 - 21:47

333

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Orthonormal set in $L^2(0,1)$ that is not complete

Published on 16 Oct 2019 - 22:16

569

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Proof of $\|P\| \leq \|I-P\|$ for L2 norm in Hilbert space when $P$ is a projection

Published on 29 Mar 2026 - 5:33

54

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On surjective operators

Published on 17 Oct 2019 - 15:12

52

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dimension of an infinite-dimensional Banach space is $\geq c $.

Published on 02 Apr 2026 - 0:17

56

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Closed Hilbert subspace S with $S^\perp=\{0\}$

Published on 18 Oct 2019 - 6:08

41

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Finding orthogonal of a set in functional analysis

Published on 18 Oct 2019 - 12:08

35

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Show that there exists $x \in \mathcal{H}$ such that $\langle x,e_n \rangle = \alpha^n$

Published on 18 Oct 2019 - 12:21

436

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Weak closure of orthonormal basis in Hilbert space (2)

Published on 01 Apr 2026 - 10:29

List Question

Weak closure of orthonormal basis in Hilbert space

Find $\|x\|$ when $\langle x,e_k \rangle=1/2^k$

Is the point spectrum always countable?

Normal plus compact is Fredholm with index 0

How is the quotient space H/K is isomorphic to the orthogonal complement of K?

Do the transpose operator and the adjoint operator have same ranges and kernels?

Relation between two subspaces

Orthonormal set in $L^2(0,1)$ that is not complete

Proof of $\|P\| \leq \|I-P\|$ for L2 norm in Hilbert space when $P$ is a projection

On surjective operators

dimension of an infinite-dimensional Banach space is $\geq c $.

Closed Hilbert subspace S with $S^\perp=\{0\}$

Finding orthogonal of a set in functional analysis

Show that there exists $x \in \mathcal{H}$ such that $\langle x,e_n \rangle = \alpha^n$

Weak closure of orthonormal basis in Hilbert space (2)

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