Non- (quantum) differentiable $C^1$-functions in the spaces with trivial Boyd indices

Details Non- (quantum) differentiable $C^1$-functions in the spaces with trivial Boyd indices Non- (quantum) differentiable $C^1$-functions in the spaces with trivial Boyd indices

2008-08-21

arxiv.org/abs/0808.2856v1

Integral Equations Operator Theory 57 (2007), no. 2, 247--261

Mathematics

Functional Analysis

15 pages

Scientific paper

If E is a separable symmetric sequence space with trivial Boyd indices and
$\cC^E$ is the corresponding ideal of compact operators, then there exists a
$C^1$-function $f_E$, a self-adjoint element $W\in \cC^E$ and a densely defined
closed symmetric derivation $\delta$ on $\cC^E$ such that $W \in Dom \delta$,
but $f_E(W) \notin Dom \delta$.

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