List questions from self-adjoint-operators

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A problem about operators on an Euclidean space

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Unitary operator as an exponent of self-adjoint

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For which $C$ is the linear map $\varphi_C : V \to V, A \mapsto CA$ selfadjoint with scalar product $\langle A, B \rangle = \operatorname{tr}(A^t B)$?

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Self adjoint extensions

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Concept of 2-variable function for operators on an $n$-dimensional inner product space

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self-adjoint operator and symmetric operator

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Infinite-dimensional inner product spaces: if $A^k = I$ for self-adjoint $A$ and for integer $k > 0$, then $A^2 = I$

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Determine representation matrix of orthogonal projection

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Prove that $v = 0 \iff v + iT(v) = 0$ for a self adjoint operator

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show that Norm of v+iT(v) equals to the Norm of v-iT(v)

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Show the operator $I-iT$ is invertible and that $(I-iT)(I+iT)^{-1}$ is unitary operator

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If $T$ is self-adjoint and $\langle T(u),u \rangle > 0$ for every $u$ in $K$, $u\neq0$ then $T = R^2$ for some self-adjoint non-singular operator $R$

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prove that an operator is unitary

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n-th Power of a self-adjoint linear operator

Published on 22 Jun 2020 - 19:47

List Question

Operators on an Euclidean space

A problem about operators on an Euclidean space

Unitary operator as an exponent of self-adjoint

For which $C$ is the linear map $\varphi_C : V \to V, A \mapsto CA$ selfadjoint with scalar product $\langle A, B \rangle = \operatorname{tr}(A^t B)$?

Self adjoint extensions

Concept of 2-variable function for operators on an $n$-dimensional inner product space

self-adjoint operator and symmetric operator

Infinite-dimensional inner product spaces: if $A^k = I$ for self-adjoint $A$ and for integer $k > 0$, then $A^2 = I$

Determine representation matrix of orthogonal projection

Prove that $v = 0 \iff v + iT(v) = 0$ for a self adjoint operator

show that Norm of v+iT(v) equals to the Norm of v-iT(v)

Show the operator $I-iT$ is invertible and that $(I-iT)(I+iT)^{-1}$ is unitary operator

If $T$ is self-adjoint and $\langle T(u),u \rangle > 0$ for every $u$ in $K$, $u\neq0$ then $T = R^2$ for some self-adjoint non-singular operator $R$

prove that an operator is unitary

n-th Power of a self-adjoint linear operator

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