8,551 research outputs found
Third Order Trace Formula
In (J. Funct. Anal. 257, 1092-1132 (2009)), Dykema and Skripka showed the
existence of higher order spectral shift functions when the unperturbed
self-adjoint operator is bounded and the perturbations is Hilbert-Schmidt. In
this article, we give a different proof for the existence of spectral shift
function for the third order when the unperturbed operator is self-adjoint
(bounded or unbounded, but bounded below).Comment: 26 page
Inner multipliers and Rudin type invariant subspaces
Let be a Hilbert space and be
the -valued Hardy space over the unit disc in
. The well known Beurling-Lax-Halmos theorem states that every
shift invariant subspace of other than
has the form , where is an
operator-valued inner multiplier in for some Hilbert space . In this
paper we identify with -valued Hardy
space and classify all such inner
multiplier for which is a Rudin type invariant subspace of
.Comment: 8 page
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