Arrowhead operators on a Hilbert space

Abstract

The arrowhead matrices define a class of one-term Sylvester matrix (OTSM) operators on a finite-dimensional Hilbert space through an elementary UDL factorization. It enables us to consider the infinite invertible arrowhead matrices UDL factored properly for introducing, under suitable conditions, the arrowhead operators
and their associated class of OTSM operators on an infinite-dimensional Hilbert space. Properties regarding convergence, inertia, inverses, and spectra are also considered.

Full text

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Volume 10, Number 3 (2016), 593–609 doi:10.7153/oam-10-34
ARROWHEAD OPERATORS ON A HILBERT SPACE
J. ABDERRAM ´
AN MARRERO AND V. T OMEO
Abstract. The arrowhead matrices define a class of one-term Sylvester matrix (OTSM) operators
on a finite-dimensional Hilbert space through an elementary UDL factorization. It enables us
to consider the infinite invertible arrowhead matrices UDL factored properly for introducing,
under suitable conditions, the arrowhead operators and their associated class of OTSM operators
on an infinite-dimensional Hilbert space. Properties regarding convergence, inertia, inverses, and
spectra are also considered.
Mathematics subject classification (2010): 15A99, 47B99.
Keywords and phrases:Infinite arrowhead matrix, matrix factorization, arrowhead operator, one-term
Sylvester matrix operator.
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