共查询到20条相似文献,搜索用时 62 毫秒
1.
T. Hara 《Integral Equations and Operator Theory》1995,23(2):179-204
A bounded linear operatorT is a numerical contraction if and only if there exists a selfadjoint contractionZ such that
. The aim of the present paper is to study the structure of the coreZ(T) of all selfadjoint contractions satisfying the above inequality. Especially we consider several conditions for thatZ(T) is a single-point set. By using this argument we shall characterize extreme points of the set of all numerical contractions. Moreover we shall give effective sufficient conditions for extreme points. 相似文献
2.
We consider parabolic variational inequalities having the strong formulation
where
for some admissible initial datum, V is a separable Banach space with separable dual
is an appropriate monotone operator, and
is a convex,
lower semicontinuous functional. Well-posedness of (1) follows from an explicit construction of the related semigroup
Illustrative applications to free boundary problems and to parabolic problems in Orlicz-Sobolev spaces are given. 相似文献
((1)) |
3.
Suppose A generates a strongly continuous linear group
on a Banach space X and B is a linear operator on X. It is shown that an extension of
generates a strongly continuous semigroup if and only if the family of operators
has an appropriate evolution system. This produces simple sufficient conditions for an extension of
to generate a strongly continuous semigroup, including
相似文献
(1) | being m-dissipative and for all x in the domain of B; or | ||
(2) |
being m-dissipative and
being a commuting family of operators with
|
4.
Vladimír Müller 《Integral Equations and Operator Theory》1992,15(6):1033-1041
If belongs to the essential approximate point spectrum of a Banach space operatorTB(X) and
is a sequence of positive numbers with lim
j
a
j
=0, then there existsxX such that
for every polynomialp. This result is the best possible — if
for some constantc>0 thenT has already a non-trivial invariant subspace, which is not true in general. 相似文献
5.
Suppose that is a trigonometric polynomial of the form (z) = Nn=-N an zn. It is well-known that T is normal if and only if | a– N| = | aN| and the Fourier coefficients of satisfy the following symmetry condition:
In this paper we provide a complete criterion for hyponormality of T when satisfies a partial symmetry condition:
相似文献
6.
A linear operatorT L(H) is called a strongly irreducible, if there is no non-trivial idempotent linear operator commuting withT. In this paper, denote the set of all strongly irreducible operators by (SI). Let
be a nest with infinite dimensional atoms,
be the nest algebra associated with
and
be the closure of
, then the following result is proved
.The projection partially supported by Chinese Natural Science Foundation and Fund of Laboratory of Nonlinear Mathematical Modeling and Methods in Fudan University in Shanghai P.R.C. 相似文献
7.
We introduce the notion ofweak subnormality, which generalizes subnormality in the sense that for the extension
ofT
we only require that
hold forf
; in this case we call
a partially normal extension ofT. After establishing some basic results about weak subnormality (including those dealing with the notion of minimal partially normal extension), we proceed to characterize weak subnormality for weighted shifts and to prove that 2-hyponormal weighted shifts are weakly subnormal. Let {
n
}
n=0
be a weight sequence and letW
denote the associated unilateral weighted shift on
. IfW
is 2-hyponormal thenW
is weakly subnormal. Moreover, there exists a partially normal extension
on
such that (i)
is hyponormal; (ii)
; and (iii)
. In particular, if is strictly increasing then
can be obtained as
whereW
is a weighted shift whose weight sequence {
n
·
n=0
is given by
In this case,
is a minimal partially normal extension ofW
. In addition, ifW
is 3-hyponormal then
can be chosen to be weakly subnormal. This allows us to shed new light on Stampfli's geometric construction of the minimal normal extension of a subnormal weighted shift. Our methods also yield two additional results: (i) the square of a weakly subnormal operator whose minimal partially normal extension is always hyponormal, and (ii) a 2-hyponormal operator with rank-one self-commutator is necessarily subnormal. Finally, we investigate the connections of weak subnormality and 2-hyponormality with Agler's model theory.Supported by NSF research grant DMS-9800931.Supported by the Brain Korea 21 Project from the Korean Ministry of Education. 相似文献
8.
Pei Yuan Wu 《Integral Equations and Operator Theory》2006,56(4):559-569
Let A be a bounded linear operator on a complex separable Hilbert space H. We show that A is a C0(N) contraction if and only if
, where U is a singular unitary operator with multiplicity
and x1, . . . , xd are orthonormal vectors satisfying
. For a C0(N) contraction, this gives a complete characterization of its polar decompositions with unitary factors. 相似文献
9.
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
10.
Vincent Cachia Hagen Neidhardt Valentin A. Zagrebnov 《Integral Equations and Operator Theory》2001,39(4):396-412
We study the operator-norm error bound estimate for the exponential Trotter product formula in the case of accretive perturbations. LetA be a semibounded from below self-adjoint operator in a separable Hilbert space. LetB be a closed maximal accretive operator such that, together withB
*, they are Kato-small with respect toA with relative bounds less than one. We show that in this case the operator-norm error bound estimate for the exponential Trotter product formula is the same as for the self-adjointB [12]:
We verify that the operator—(A+B) generates a holomorphic contraction semigroup. One gets similar results whenB is substituted byB
*.To the memory of Tosio Kato 相似文献
11.
12.
In this paper we show that if X is an s-distance set in
m
and X is on
p concentric spheres then
Moreover if
X is antipodal, then
. 相似文献
13.
Ariyadasa Aluthge 《Integral Equations and Operator Theory》1996,24(4):497-501
A bounded linear operatorT is calledp-Hyponormal if (T
*T)p(TT
*)p, 0<p1. In Aluthge [1], we studied the properties of p-hyponormal operators using the operator
. In this work we consider a more general operator
, and generalize some properties of p-hyponormal operators obtained in [1]. 相似文献
14.
Atsushi Uchiyama 《Integral Equations and Operator Theory》1999,33(2):221-230
For an-multicyclicp-hyponormal operatorT, we shall show that |T|2p
–|T
*|2p
belongs to the Schatten
and that tr
Area ((T)). 相似文献
15.
The spectrum determined growth property ofC
0 semigroups in a Banach space is studied. It is shown that ifA generates aC
0 semigroup in a Banach spaceX, which satisfies the following conditions: 1) for any >s(A), sup{R(;A) | Re}<; 2) there is a 0>(A) such that
, xX, and
, fX
*, then (A=s(A). Moreover, it is also shown that ifA=A
0+B is the infinitesimal generator of aC
0 semigroup in Hilbert space, whereA
0 is a discrete operator andB is bounded, then (A)=s(A). Finally the results obtained are applied to wave equation and thermoelastic system. 相似文献
16.
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
17.
B. I. Peleshenko 《Ukrainian Mathematical Journal》2000,52(7):1134-1140
We consider the integral convolution operators
\varepsilon } {k\left( {x - y} \right)f\left( y \right)dy}$$
" align="middle" border="0">
defined on spaces of functions of several real variables. For the kernels k(x) satisfying the Hörmander condition, we establish necessary and sufficient conditions under which the operators {T
} are uniformly bounded from Lorentz spaces into Marcinkiewicz spaces. 相似文献
18.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
19.
A Littlewood-Paley type
inequality 总被引:2,自引:0,他引:2
In this note we prove the following theorem: Let u be a
harmonic function in the unit ball
and
. Then there is a
constant C =
C(p,
n) such that
. 相似文献
20.
Chang Jen-Chun Chen Rong-Jaye Hwang Frank K. 《Methodology and Computing in Applied Probability》2001,3(4):379-386
A d-within-consecutive-k-out-of-n system, abbreviated as Con(d, k, n), is a linear system of n components in a line which fails if and only if there exists a set of k consecutive components containing at least d failed ones. So far the fastest algorithm to compute the reliability of Con(d, k, n) is Hwang and Wright's
algorithm published in 1997, where
. In this paper we use automata theory to reduce
to
. For d small or close to k, we have reduced
from exponentially many (in k) to polynomially many. The computational complexity of our final algorithm is
, where
. 相似文献