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11 votes
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Von Neumann Inequality in Banach spaces

It is known that the only Banach space that satisfies the von-Neumann inequality is the Hilbert space: Theorem (see e.g. Pisier, "Similarity Problems and Completely Bounded Maps", p 27) For a Banach ...
erz's user avatar
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4 votes
0 answers
2k views

Eigenvalues and spectrum of the adjoint

In a finite-dimensional Hilbert space, the eigenvalues of the adjoint $A^*$ of an operator $A$ are the complex conjugates of the eigenvalues of $A$. But in infinite dimensions this need no longer be ...
Arnold Neumaier's user avatar
1 vote
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A point in Ion Suciu's paper on semigroups of isometric operators

My question is concerned a point in this 1968 paper by Ion Suciu which is given in Theorem 2. In the last paragraph of page 104, it is claimed that $N$ (given in the formula 2.5) is a wandering ...
ABB's user avatar
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1 vote
0 answers
220 views

About the projection on the unit sphere

Let $H$ be a Hilbert Space and let $A\subset H$ be a connected set such that any two elements of $A$ are linearly independent and also $A^{\bot}=\left\{0\right\}$ (this seems to be immaterial). Is ...
erz's user avatar
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0 votes
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263 views

Does AX+XA=0 have any non-trivial solutions?

Let $X$ be a continuous linear self-adjoint operator on some Hilbert space $H$ and for arbitrary compact operators $A$ we have: $XA+AX=0.$ Does this imply that $X=0$ or can there be non-trivial ...
Kinzlin's user avatar
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