The block numerical range of analytic operator functions

Radl, Agnes; Tretter, Christiane; Wagenhofer, Markus (2014). The block numerical range of analytic operator functions. Operators and Matrices, 8(4), pp. 901-934. Element 10.7153/oam-08-51

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We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Radl, Agnes and Tretter, Christiane

Subjects:

500 Science > 510 Mathematics

ISSN:

1846-3886

Publisher:

Element

Language:

English

Submitter:

Mario Amrein

Date Deposited:

14 Apr 2015 15:00

Last Modified:

14 Apr 2015 15:00

Publisher DOI:

10.7153/oam-08-51

BORIS DOI:

10.7892/boris.66704

URI:

https://boris.unibe.ch/id/eprint/66704

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