Question

Why is the infinite dimensional vector space with only finitely many nonvanishing components incomplete?

score 268 · Answer 1 · 2014-09-25 23:00:11

268

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Why is the infinite dimensional vector space with only finitely many nonvanishing components incomplete?

Published on 25 Sep 2014 - 23:00

score 136 · Answer 2 · 2014-09-26 07:52:25

136

Views

Sum of closed linear subspaces necessarily closed?

Published on 26 Sep 2014 - 7:52

score 111 · Answer 3 · 2026-03-26 19:37:30

111

Views

Subalgebra generated by selfadjoint operator $A_0\in\mathscr{L}(H,H)$

Published on 26 Mar 2026 - 19:37

score 320 · Answer 4 · 2026-03-25 11:22:45

320

Views

Show that Polynomials Are Complete on the Real Line

Published on 25 Mar 2026 - 11:22

score 319 · Answer 5 · 2026-04-01 03:13:20

319

Views

Spectral Measures: Integration

Published on 01 Apr 2026 - 3:13

score 115 · Answer 6 · 2026-03-27 07:13:49

115

Views

The projection operator defined by $(P_n(h) - h, v)_H = 0$

Published on 27 Mar 2026 - 7:13

score 2.6k · Answer 7 · 2014-09-29 21:34:18

2.6k

Views

Can we have infinite-dimensional separable Hilbert spaces?

Published on 29 Sep 2014 - 21:34

score 856 · Answer 8 · 2026-03-29 03:45:07

856

Views

Why coefficients of Fourier series are countable, though the initial periodic function is described with an uncountable set of points

Published on 29 Mar 2026 - 3:45

score 1.3k · Answer 9 · 2026-03-31 03:28:12

1.3k

Views

Over ZF, does "every Hilbert space have a basis" imply AC?

Published on 31 Mar 2026 - 3:28

score 34 · Answer 10 · 2014-09-30 14:27:47

34

Views

If $y_m \to y$ in $H$ then $|y_m|_H \leq C|y|$ for this sequence?

Published on 30 Sep 2014 - 14:27

score 378 · Answer 11 · 2014-09-30 21:42:43

378

Views

When a symmetric densely defined operator is an adjoint operator?

Published on 30 Sep 2014 - 21:42

score 496 · Answer 12 · 2026-03-29 13:40:57

496

Views

Is the (first order theory) of Hilbert spaces categorical?

Published on 29 Mar 2026 - 13:40

score 123 · Answer 13 · 2014-10-02 14:15:09

123

Views

product of one dimensional basis functions spanning two dimensional space

Published on 02 Oct 2014 - 14:15

score 246 · Answer 14 · 2026-03-25 15:50:22

246

Views

Questions about open balls and convergence in Hilbert space

Published on 25 Mar 2026 - 15:50

score 1k · Answer 15 · 2014-10-03 12:10:40

1k

Views

Existence of Unitary Operator which Extends any inner product preserving operator in a Hilbert Space

Published on 03 Oct 2014 - 12:10

List Question

Why is the infinite dimensional vector space with only finitely many nonvanishing components incomplete?

Sum of closed linear subspaces necessarily closed?

Subalgebra generated by selfadjoint operator $A_0\in\mathscr{L}(H,H)$

Show that Polynomials Are Complete on the Real Line

Spectral Measures: Integration

The projection operator defined by $(P_n(h) - h, v)_H = 0$

Can we have infinite-dimensional separable Hilbert spaces?

Why coefficients of Fourier series are countable, though the initial periodic function is described with an uncountable set of points

Over ZF, does "every Hilbert space have a basis" imply AC?

If $y_m \to y$ in $H$ then $|y_m|_H \leq C|y|$ for this sequence?

When a symmetric densely defined operator is an adjoint operator?

Is the (first order theory) of Hilbert spaces categorical?

product of one dimensional basis functions spanning two dimensional space

Questions about open balls and convergence in Hilbert space

Existence of Unitary Operator which Extends any inner product preserving operator in a Hilbert Space

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