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Let $H$ be a Hilbert space and $B(H)$ be the space of all bounded operators on $H$. The Wold decomposition says that: an operator $x$ in $B(H)$ is an isometry if and only if $x=x_u\oplus x_s$ where $...

A is said to be elementary if A is isomorphic to some $K(H)$ or $M_n$. A C*-subalgebra $B$ is said to be hereditary if for every $0≤a≤b∈B$ we have $a∈B$. I wanted to know that is this statement true? ...

Given a graded Hilbert space $\mathbf{H} = \bigoplus_{k \in \mathbb{N}} \mathbf{H}_k$, one might extend the notion of adjoint to a "graded adjoint" defined as follows: $L \in B(\mathbf{H})$ is said to ...