Journal of Operator Theory
Volume 72, Issue 2, Fall 2014 pp. 451-473.
Function theory and spectral mapping theorems for
antilinear operators
Authors:
Marko Huhtanen (1)
and Allan Peramaki (2)
Author institution: (1) Division of Mathematics,
Department of Electrical and Information Engineering,
University of Oulu, 90570 Oulu 57,
Finland
(2) Department of Mathematics and Systems Analysis,
Aalto University, Box 1100, FIN-02015,
Finland
Summary: Unlike in complex linear operator theory,
polynomials or, more generally, Laurent series
of antilinear operators cannot be modelled with complex
analysis. There exists a corresponding function space, though,
surfacing in spectral mapping theorems.
These spectral mapping theorems are inclusive in general. Equality
can be established in the self-adjoint case.
The arising functions
are shown to possess a biradial character.
It is shown that to any
given set of Jacobi
parameters corresponds a biradial measure
yielding these parameters in an iterative orthogonalization
process in this function space, once equipped with the corresponding $L^2$
structure.
DOI: http://dx.doi.org/10.7900/jot.2013may20.1991
Keywords: antilinear operator, Laurent series, spectral mapping,
biradial function, biradial measure, Jacobi operator,
Hankel operator
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