3,020 research outputs found
Topological radicals, V. From algebra to spectral theory
We introduce and study procedures and constructions in the theory of the
joint spectral radius that are related to the spectral theory. In particular we
devlop the theory of the scattered radical. Among applications we find some
sufficient conditions of continuity of the spectrum and spectral radii of
various types, and prove that in GCR C*-algebras the joint spectral radius is
continuous on precompact subsets and coincides with the Berger-Wang radius
Topological radicals, II. Applications to spectral theory of multiplication operators
We develop the spectral radius technique and the theory of tensor radicals.
As applications we obtain numerous results on mutiplication operators in Banach
algebras and Operator bimodules
Reduced spectral synthesis and compact operator synthesis
We introduce and study the notion of reduced spectral synthesis, which
unifies the concepts of spectral synthesis and uniqueness in locally compact
groups. We exhibit a number of examples and prove that every non-discrete
locally compact group with an open abelian subgroup has a subset that fails
reduced spectral synthesis. We introduce compact operator synthesis as an
operator algebraic counterpart of this notion and link it with other
exceptional sets in operator algebra theory, studied previously. We show that a
closed subset of a second countable locally compact group satisfies
reduced local spectral synthesis if and only if the subset of satisfies compact operator synthesis. We apply
our results to questions about the equivalence of linear operator equations
with normal commuting coefficients on Schatten -classes.Comment: 43 page
Closable Multipliers
Let (X,m) and (Y,n) be standard measure spaces. A function f in
is called a (measurable) Schur multiplier if
the map , defined on the space of Hilbert-Schmidt operators from
to by multiplying their integral kernels by f, is bounded
in the operator norm.
The paper studies measurable functions f for which is closable in the
norm topology or in the weak* topology. We obtain a characterisation of
w*-closable multipliers and relate the question about norm closability to the
theory of operator synthesis. We also study multipliers of two special types:
if f is of Toeplitz type, that is, if f(x,y)=h(x-y), x,y in G, where G is a
locally compact abelian group, then the closability of f is related to the
local inclusion of h in the Fourier algebra A(G) of G. If f is a divided
difference, that is, a function of the form (h(x)-h(y))/(x-y), then its
closability is related to the "operator smoothness" of the function h. A number
of examples of non-closable, norm closable and w*-closable multipliers are
presented.Comment: 35 page
Secondary electron emission from sodium chloride, glass and aluminum oxide at various temperature
The method of single impulses was used to measure the coefficients of the secondary electronic emission for 2 types of Al2O2, monocrystalline NaCl and glass at different temperatures and for different values of the energy of the primary electrons. The value of the secondary electron emission does not depend upon temperature. The effect of a gas film on the value of the secondary electron emission was detected
Some remarks on invariant subspaces in real Banach spaces (revised version)
It is proved that a commutative algebra of operators on a reflexive real
Banach space has an invariant subspace if each operator satisfies the
condition where is the essential norm. This
implies the existence of an invariant subspace for every commutative family of
essentially selfadjoint operators on a real Hilbert space
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