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Compact differences of composition operators on weighted Dirichlet spaces

100%

Allen R., Heller K., Pons M.

Open Mathematics

2014

tom 12

nr 7

1040-1051

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

Unbounded Hermitian operators and relative reproducing kernel Hilbert space

68%

Jorgensen P.

Open Mathematics

2010

tom 8

nr 3

569-596

We study unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency indices, and associated deficiency spaces; but in practical problems, the direct computation of these indices can be difficult. Instead, in this paper we identify additional structures that throw light on the problem. We will attack the problem of computing deficiency spaces for a single Hermitian operator with dense domain in a Hilbert space which occurs in a duality relation with a second Hermitian operator, often in the same Hilbert space.

Ograniczanie wyników

2 Open Mathematics

1 Allen R.

1 Heller K.

1 Jorgensen P.

1 Pons M.

1 2014

1 2010

Wyniki wyszukiwania

Compact differences of composition operators on weighted Dirichlet spaces

Unbounded Hermitian operators and relative reproducing kernel Hilbert space