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1.
Aluthge transforms of operators 总被引:7,自引:0,他引:7
Associated with every operatorT on Hilbert space is its Aluthge transform
(defined below). In this note we study various connections betweenT and
, including relations between various spectra, numerical ranges, and lattices of invariant subspaces. In particular, we show that if
has a nontrivial invariant subspace, then so doesT, and we give various applications of our results. 相似文献
2.
Roman Drnovšek 《Integral Equations and Operator Theory》2001,39(3):253-266
Let
be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that
is finitely quasinilpotent at a vectorx
0X whenever for any finite subset
of
the joint spectral radius of
atx
0 is equal 0. If such collection
contains a non-zero compact operator, then
and its commutant
have a common non-trivial invariant, subspace. If in addition,
is a collection of positive operators on a Banach lattice, then
has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let
be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then
has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia. 相似文献
3.
Takuya Hara 《Integral Equations and Operator Theory》1992,15(4):551-567
Let
be a Hilbert space. A continuous positive operatorT on
uniquely determines a Hilbert space
which is continuously imbedded in
and for which
with the canonical imbedding
. A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space (
) which is continuously imbedded in
and for which
with the canonical imbedding
. 相似文献
4.
Graeme West 《Integral Equations and Operator Theory》1995,22(3):352-359
Suppose
is a von Neumann algebra on a Hilbert space
and
is any ideal in
. We determine a topology
on
, for which the members of
that are
to norm continuous are exactly those in
; and a bornology
on
such that the elements of
which map the unit ball to an element of
, equivalently those members of
that are norm to
bounded, are exactly those in
. This is achieved via analogues of the notions of injectivity and surjectivity in the theory of operator ideals on Banach spaces. 相似文献
5.
D. N. Dudin 《Mathematical Notes》1968,3(1):42-44
For an algebra
of subsets of a set X there is constructed a set
and an algebra of its subsets so that the mapping
is a one-to-one correspondence between
and
and for each additive measure on
the measure
on
defined by the equation
is countably additive.Translated from Matematicheskie Zametki, Vol. 3, No. 1, pp. 71–76, January, 1968.The author wishes to express his deep appreciation to S. V. Fomin, under whose guidance this paper was written. 相似文献
6.
William M. McGovern 《Inventiones Mathematicae》1989,97(1):209-217
Summary LetG be a complex semisimple algebraic group with Lie algebra
. Let
be a nilpotentG-orbit,
its ring of regular functions. We derive a formula for
as aG-module and prove some partial results on
a cover of
. We then relate this formula to various existing multiplicity formulas forK-types in Harish-Chandra bimodules ofG.Supported by National Science Foundation Grant DMS-8505550 相似文献
7.
Xingde Dai 《Integral Equations and Operator Theory》1997,27(3):294-313
Let be a nest in a separably acting factor
. We present conditions for a factor
to be a bimodule of the nest subalgebraalgß in
which is singly generated in the norm topology. Some relevant results about the compact ideal
, the quasitriangular algebra and the Calkin algebra are established.This work was supported, in part, by funds provided by the University of North Carolina at Charlotte. 相似文献
8.
We consider the on-line computation of the lattice of maximal antichains of a finite poset
. This on-line computation satisfies what we call the linear extension hypothesis: the new incoming vertex is always maximal in the current subposet of
. In addition to its theoretical interest, this abstraction of the lattice of antichains of a poset has structural properties which give it interesting practical behavior. In particular, the lattice of maximal antichains may be useful for testing distributed computations, for which purpose the lattice of antichains is already widely used. Our on-line algorithm has a run time complexity of
, where |P| is the number of elements of the poset,
, |MA(P)| is the number of maximal antichains of
and (P) is the width of
. This is more efficient than the best off-line algorithms known so far. 相似文献
9.
Peter Raith 《Journal d'Analyse Mathématique》1999,78(1):117-142
Assume thatX is a finite union of closed intervals and consider aC
1-mapX→ℝ for which {c∈X: T′c=0} is finite. Set
. Fix ann ∈ ℕ. For ε>0, theC
1-map
is called an ε-perturbation ofT if
is a piecewise monotonic map with at mostn intervals of monotonicity and
is ε-close toT in theC
1-topology. The influence of small perturbations ofT on the dynamical system (R(T),T) is investigated. Under a certain condition on the continuous functionf:X → ℝ, the topological pressure is lower semi-continuous. Furthermore, the topological pressure is upper semi-continuous for
every continuous functionf:X → ℝ. If (R(T),T) has positive topological entropy and a unique measure μ of maximal entropy, then every sufficiently small perturbation
ofT has a unique measure
of maximal entropy, and the map
is continuous atT in the weak star-topology. 相似文献
10.
Wolfgang Henke 《manuscripta mathematica》1976,19(2):165-188
Let M, resp.
, denote Riemannian manifolds of dimensions m>4, resp.
=m+2, and of constant sectional curvatures C, resp.
, with
0 and
is a standard space form, then the foliation L is a (globally) trivial fibre bundle with fibre Sm–1. 相似文献
11.
Negami and Kawagoe has already defined a polynomial
associated with each graphG as what discriminates graphs more finely than the polynomialf(G) defined by Negami and the Tutte polynomial. In this paper, we shall show that the polynomial
includes potentially the generating function counting the independent sets and the degree sequence of a graphG, which cannot be recognized fromf(G) in general, and discuss on
of treesT with observations by computer experiments. 相似文献
12.
Dr. John Walsh 《Probability Theory and Related Fields》1970,14(3):169-188
Summary In this paper we treat a time-symmetrical Martin boundary theory for continuous parameter Markov chains. This is done by reversing the time sense of a Markov chainX
t
in such a way as to obtain a dual Markov chain
, and considering the two chains together. Various relations between the Martin exit boundaries
and
of these processes are studied. The exit boundary
of
, is in a sense an entrance boundary forX
t
and vice versa. After a natural identification of certain points in
and
one can topologizeI
in such a way thatboth X
t and
have standard modifications in this space which are right continuous, have left limits, and are strongly Markov.Research supported in part at Stanford University, Stanford, California under AFOSR 0049. 相似文献
13.
Prof. Ottmar Loos 《Monatshefte für Mathematik》1978,86(2):107-129
Every Jordan pair
defines an algebraic varietyX containing
as a dense open subset.X is projective (affine) if and only if
is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of
. If
is separable then the automorphism group ofX is the projective group of
. 相似文献
14.
Summary We study the Hellinger type distances
on a filtered space. Herep2 is an arbitrary number andP
T
and
are two probability measures stopped at a random timeT. We give lower and upper bounds for
in predictable terms. 相似文献
15.
Scott McCullough 《Integral Equations and Operator Theory》2001,39(3):335-362
Let
denote an annulus,E a finite subset of
with at least three elements, and
the ideal of functions in
which vanish at the points ofE. The quotient
does not have a completely isometric representation on a finite dimensional Hilbert space. This complements a result of [11] which implies that the quotient has an isometric representation on a Hilbert space of dimension twice the cardinality ofE. 相似文献
16.
Ignacio Bajo 《Monatshefte für Mathematik》1994,118(1-2):1-6
Let
be a complex Lie algebra,
its underlying real Lie algebra,
a real form of
and ·, · the euclidean product induced by the real part of an hermitian inner product on
. Let aut
be the Lie algebra of skew-symmetric derivations of
. We give necessary and sufficient conditions to ensure that aut
is composed of skew-hermitian derivations. As an application, we study holomorphy in large subgroups of isometries of Lie groups. 相似文献
17.
J. Hartmann 《Transformation Groups》2001,6(2):157-164
Let :GGl(n,
) be a representation of a finite groupG over a field
such that the ring of invariants
is a polynomial algebra
. It is known that in the nonmodular case (i.e., when the order of the group is not divisible by the characteristic of
), the invariants ofG acting on the tensor product
of a polynomial and an exterior algebra are given by
,d denoting the exterior derivative. We show that in the modular case, the ring of invariants in
is of this form if and only if
is a polynomial algebra and all pseudoreflections in (G) are diagonalizable. 相似文献
18.
N. L. Vasilevski 《Integral Equations and Operator Theory》1999,34(1):107-126
Let
be the unit disk in,
be the Bergman space, consisting of all analytic functions from
, and
be the Bergman projection of
onto
. We constructC
*-algebras
, for functions of which the commutator of Toeplitz operators [T
a
,T
b
]=T
a
T
b
–T
b
T
a
is compact, and, at the same time, the semi-commutator [T
a
,T
b
)=T
a
T
b
–T
ab
is not compact.It is proved, that for each finite set =n
0,n
1, ...,n
m
, where 1=n
0
1
<...
m
, andn
k
{}, there are algebras
of the above type, such that the symbol algebras Sym
of Toeplitz operator algebras
arecommutative, while the symbol algebras Sym
of the algebras
, generated by multiplication operators
and
, haveirreducible representations exactly of dimensions n
0,n
1,..., n
m
.This work was partially supported by CONACYT Project 3114P-E9607, México. 相似文献
19.
LetT be a contraction acting in a separable Hilbert space
and leaving invariant a nest
of subspaces of
. We answer the question: when doesT have an isometric extension to
which leaves invariant the nest
= {N N :N
;}. 相似文献
20.
Paul H. Schuette 《Journal of Theoretical Probability》1994,7(1):3-45
Given a sequence of independent, but not necessarily identically distributed random variables,Y
i
, letS
k
denote thekth partial sum. Define a function
by taking
to be the piecewise linear interpolant of the points (k, S
k
), evaluated att, whereS
0=0, andk=0, 1, 2,... Fort[0, 1], let
. The
are called trajectories. With regularity and moment conditions on theY
i
, a large deviation principle is proved for the
. 相似文献