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Spectral Theory of Linear Operators - and Spectral Systems in Banach Algebras (Hardcover, 2nd ed. 2007)
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Spectral Theory of Linear Operators - and Spectral Systems in Banach Algebras (Hardcover, 2nd ed. 2007)
Series: Operator Theory: Advances and Applications, 139
Expected to ship within 12 - 19 working days
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Spectral theoryis an important part of functional analysis.It has
numerousapp- cations in many parts of mathematics and physics
including matrix theory, fu- tion theory, complex analysis,
di?erential and integral equations, control theory and quantum
physics. In recent years, spectral theory has witnessed an
explosive development. There are many types of spectra, both for
one or several commuting operators, with important applications,
for example the approximate point spectrum, Taylor spectrum, local
spectrum, essential spectrum, etc. The present monograph is an
attempt to organize the available material most of which exists
only in the form of research papers scattered throughout the
literature. The aim is to present a survey of results concerning
various types of spectra in a uni?ed, axiomatic way. The central
unifying notion is that of a regularity, which in a Banach algebra
isasubsetofelementsthatareconsideredtobe nice
.AregularityRinaBanach algebraA de?nes the corresponding spectrum ?
(a)={ C: a / ? R} in R the same wayas the ordinaryspectrum is
de?ned by means of invertible elements, ?(a)={ C: a / ? Inv(A)}.
Axioms of a regularity are chosen in such a way that there are many
natural interesting classes satisfying them. At the same time they
are strong enough for non-trivial consequences, for example the
spectral mapping theorem. Spectra ofn-tuples ofcommuting elements
ofa Banachalgebraaredescribed similarly by means of a notion of
joint regularity. This notion is closely related to ? the axiomatic
spectral theory of Zelazko and S lodkowski."
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