# Tagged Questions

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### Question about the Averson's proof of the bicommutant theorem.

In the Averson's proof of the bicommutant theorem is proved that, if $A$ is a self-adjoint algebra of operators with trivial null space and $T \in A''$, for every $\epsilon>0$, $n=1,2..$ and every ...
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### Canonical Forms For Matrices

In the following paper by Wedderburn what are the restrictions on the field $\mathbb F$ or on the linear application $\varphi$ that the author refers to obtain the matrix B? ...
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### Simple Modules over the Weyl Algebra

Let $k$ be a field of characteristic zero and let $A_1=k\langle x,y| \, xy-yx=1 \rangle$ be the Weyl algebra. Is there a (more or less explicit) possibility of writing down all simple modules over ...
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### Question about the essential spectrum of a negative difinite operator

please on an infinite dimensional Hilbert space how to difine the essential spectrum of an operator which is negative definite ??? Please help me Thank you.
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### H P S class operators and their inequalities

First few definitions: $A \in I(K)$ iff $A$ is isomorphic to some member of $K$ $A \in S(K)$ iff $A$ is a subalgebra of some member of $K$ $A \in H(K)$ iff $A$ is a homomorphic image of some ...
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### Inequality of Class operators H S and P

First few definitions: $A \in I(K)$ iff $A$ is isomorphic to some member of $K$ $A \in S(K)$ iff $A$ is a subalgebra of some member of $K$ $A \in H(K)$ iff $A$ is a homomorphic image of some ...
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### relations between two linear operators

Let $\alpha,\beta$ be linear operators on a finite dimensional vector space $V$ over field $F$. Let $\gamma=\alpha\circ\beta$ and $\delta=\beta\circ\alpha$. Prove that: (1). $m_\delta(x)$ divides ...
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### A question about tensor product of algebras of compact operators. [duplicate]

Let $\cal{H}$ be a separable Hilbert space and $\cal{K(\cal{H})}$ the algebra of compact operators acting on $\cal{H}$. Then $$\cal{K(\cal{H})}\otimes\cal{K}(\cal{H})\cong\cal{K}(\cal{H}\otimes H).$$ ...
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### Does ternary operations have associative property?

Binary Operation is a function. Right? We know that all Binary operations have associative property. They must be either associative or non-associative. The condition is : $$(a*b)*c = a*(b*c)$$ ...
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### Matrix norm of a normal matrix

A normal matrix defined over a complex vector space has the property, that $\|A\|_2$ is its largest eigenvalue and now I was wondering whether this is also true for matrices defined over the real ...
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### $(P\Lambda P^{-1}=T^2)~\implies~(\exists \Lambda'~\text{s.t.}~T=R\Lambda' R^{-1})$: $\;P,R\;$ Unitary Matrices

Let $T$ be a linear operator such that the operator $T^2$ is diagonalizable. Is $T$ necessarily diagonalizable?