Question

$\frac{\alpha}{\alpha + \beta}\|u\|^2 + \frac{\beta}{\alpha + \beta}\|v\|^2 > \langle u, v\rangle $ is true?

score 110 · Answer 1 · 2018-05-14 01:52:12

110

Views

$\frac{\alpha}{\alpha + \beta}\|u\|^2 + \frac{\beta}{\alpha + \beta}\|v\|^2 > \langle u, v\rangle $ is true?

Published on 14 May 2018 - 1:52

score 56 · Answer 2 · 2018-05-14 19:58:45

56

Views

If $A^x_n \to y$, there exists a sequence such that $A^Ay_n \to y$.

Published on 14 May 2018 - 19:58

score 41 · Answer 3 · 2018-05-15 14:07:21

41

Views

If $A : X' \rightarrow X$ and $k$ is a kernel on X, then $k$' defined by $k'(x,y) = k(A(x), A(y))$ is a kernel on $X'$ - proof help

Published on 15 May 2018 - 14:07

score 101 · Answer 4 · 2026-03-25 01:20:05

101

Views

$f_k := e_k + e_{k+1}$ complete, but $e_1 \neq \sum_{k=1}^{\infty} \alpha_k f_k$ for any $\alpha_k$

Published on 25 Mar 2026 - 1:20

score 311 · Answer 5 · 2026-03-25 11:19:04

311

Views

Orthonormal basis proof on $L_{2}[a, b]^{2}$ through Parseval's identity

Published on 25 Mar 2026 - 11:19

score 625 · Answer 6 · 2026-03-25 01:24:03

625

Views

Understanding the Core of an Operator or Map.

Published on 25 Mar 2026 - 1:24

score 88 · Answer 7 · 2018-05-16 20:53:35

88

Views

Derivative $\Lambda(\phi,\psi)=\frac{\langle\phi|A|\psi\rangle}{\langle\phi|\psi\rangle}$

Published on 16 May 2018 - 20:53

score 646 · Answer 8 · 2026-03-25 17:19:24

646

Views

Bounded sequence in a Hilbert such that all subsequences that weakly converge do so to the same limit

Published on 25 Mar 2026 - 17:19

score 655 · Answer 9 · 2018-05-17 19:11:41

655

Views

An inner product on the quotient space $F/\text{Ker}(M)$

Published on 17 May 2018 - 19:11

score 73 · Answer 10 · 2026-03-25 23:34:44

73

Views

Fourier Transform, Schwarz Space Problem

Published on 25 Mar 2026 - 23:34

score 57 · Answer 11 · 2018-05-18 14:50:24

57

Views

What is the rank of this operator?

Published on 18 May 2018 - 14:50

score 623 · Answer 12 · 2026-03-25 10:56:59

623

Views

To prove the convergence of an inner product space

Published on 25 Mar 2026 - 10:56

score 121 · Answer 13 · 2018-05-19 04:31:25

121

Views

Proving a spanning set is a closed subspace of a Hilbert Space

Published on 19 May 2018 - 4:31

score 68 · Answer 14 · 2018-05-19 12:48:05

68

Views

Why $(\operatorname{Im}(M^{1/2}), (\cdot,\cdot))$ is a Hilbert space?

Published on 19 May 2018 - 12:48

score 152 · Answer 15 · 2018-05-19 17:35:43

152

Views

Prove $||x+y||=||x||+||y||$ in a Hilbert Space

Published on 19 May 2018 - 17:35

List Question

$\frac{\alpha}{\alpha + \beta}\|u\|^2 + \frac{\beta}{\alpha + \beta}\|v\|^2 > \langle u, v\rangle $ is true?

If $A^x_n \to y$, there exists a sequence such that $A^Ay_n \to y$.

If $A : X' \rightarrow X$ and $k$ is a kernel on X, then $k$' defined by $k'(x,y) = k(A(x), A(y))$ is a kernel on $X'$ - proof help

$f_k := e_k + e_{k+1}$ complete, but $e_1 \neq \sum_{k=1}^{\infty} \alpha_k f_k$ for any $\alpha_k$

Orthonormal basis proof on $L_{2}[a, b]^{2}$ through Parseval's identity

Understanding the Core of an Operator or Map.

Derivative $\Lambda(\phi,\psi)=\frac{\langle\phi|A|\psi\rangle}{\langle\phi|\psi\rangle}$

Bounded sequence in a Hilbert such that all subsequences that weakly converge do so to the same limit

An inner product on the quotient space $F/\text{Ker}(M)$

Fourier Transform, Schwarz Space Problem

What is the rank of this operator?

To prove the convergence of an inner product space

Proving a spanning set is a closed subspace of a Hilbert Space

Why $(\operatorname{Im}(M^{1/2}), (\cdot,\cdot))$ is a Hilbert space?

Prove $||x+y||=||x||+||y||$ in a Hilbert Space

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