1,476 research outputs found
Remarks on functional calculus for perturbed first order Dirac operators
We make some remarks on earlier works on bisectoriality in of
perturbed first order differential operators by Hyt\"onen, McIntosh and Portal.
They have shown that this is equivalent to bounded holomorphic functional
calculus in for in any open interval when suitable hypotheses are
made. Hyt\"onen and McIntosh then showed that -bisectoriality in at
one value of can be extrapolated in a neighborhood of . We give a
different proof of this extrapolation and observe that the first proof has
impact on the splitting of the space by the kernel and range.Comment: 11 page
The basic sequence problem
We construct a quasi-Banach space which contains no basic sequence
Spectral characterization of sums of commutators I
Suppose \Cal J is a two-sided quasi-Banach ideal of compact operators on a
separable infinite-dimensional Hilbert space \Cal H. We show that an operator
T\in\Cal J can be expressed as finite linear combination of commutators
where A\in\Cal J and B\in\Cal B(\Cal H) if and only its eigenvalues
(arranged in decreasing order of absolute value, repeated
according to algebraic multiplicity and augmented by zeros if necessary)
satisfy the condition that the diagonal operator
\diag\{\frac1n(\lambda_1+\cdots +\lambda_n)\} is a member of \Cal J. This
answers (for quasi-Banach ideals) a question raised by Dykema, Figiel, Weiss
and Wodzicki
- …