共查询到20条相似文献,搜索用时 93 毫秒
1.
Summary.
We study certain functional equations derived from the
definition of a Jordan *-derivation pair.
More precisely, if A is a complex
*-algebra and M is a
bimodule over A, having the structure of a complex vector space
compatible with the structure of A,
such that
implies
m = 0 and
implies m
= 0 and
if
are unknown additive mappings satisfying
then E and
F can be represented by double centralizers. The
obtained result implies that one of the equations in the
definition of a Jordan *-derivation pair is redundant.
Furthermore, a remark on the extension of this result to unknown
additive mappings
such that
is given in a special case. 相似文献
2.
Noboru Okazawa 《Integral Equations and Operator Theory》2000,38(4):458-500
The imaginary powersA
it of a closed linear operatorA, with inverse, in a Banach spaceX are considered as aC
0-group {exp(itlogA);t R} of bounded linear operators onX, with generatori logA. Here logA is defined as the closure of log(1+A) – log(1+A
–1). LetA be a linearm-sectorial operator of typeS(tan ), 0(/2), in a Hilbert spaceX. That is, |Im(Au, u)| (tan )Re(Au, u) foru D(A). Then ±ilog(1+A) ism-accretive inX andilog(1+A) is the generator of aC
0-group {(1+A)
it
;t R} of bounded imaginary powers, satisfying the estimate (1+A)
it
exp(|t|),t R. In particular, ifA is invertible, then ±ilogA ism-accretive inX, where logA is exactly given by logA=log(1+A)–log(1+A
–1), and {A
it;t R} forms aC
0-group onX, with the estimate A
it exp(|t|),t R. This yields a slight improvement of the Heinz-Kato inequality. 相似文献
3.
M. Fragoulopoulou 《Periodica Mathematica Hungarica》1986,17(3):185-209
An advertibly complete locallym-convex (lmc)*-algebraE is symmetric if and only if each normed (inverse limit) factorE/N
, A, ofE is symmetric in the respective Banach factorE
, A, ofE. Every locally C*-algebra is symmetric. If denotes the continuous positive functionals on an lmc*-algebraE and withL
f
={x E: f(x
*
x) =0}, thenE is, by definition,-commutative if for anyx, y E.-commutativity and commutativity coincide in lmcC
*-algebras, so that an lmc*-algebra with a bounded approximate identity is-commutative if and only if its enveloping algebra is commutative. Several standard results for commutative lmc*-algebras are also obtained in the-commutative case, as for instance, the nonemptiness of the Gel'fand space of a suitable-commutative lmc*-algebra, the automatic continuity of positive functionals when the algebras involved factor, as well as that the spectral radius is a continuous submultiplicative semi-norm, when the algebras considered are moreover symmetric. An application of the latter result yields a spectral characterization of-commutativity. 相似文献
4.
We consider the problem
in a smooth boundary domain
, as well
as the corresponding evolution equation
. For the stationary equation
we show existence results, then we adapt the techniques of doubling of variables
to the case of the homogeneous Neumann boundary conditions and obtain the
appropriate L
1
-contraction principle and uniqueness. Subsequently, we are able to apply the
nonlinear semigroup theory and prove the L
1
-contraction principle for the associated evolution equation. 相似文献
5.
A complex number λ is an extended eigenvalue of an operator A if there is a nonzero operator X such that AX = λ XA. We characterize the set of extended eigenvalues, which we call extended point spectrum, for operators acting on finite dimensional
spaces, finite rank operators, Jordan blocks, and C0 contractions. We also describe the relationship between the extended eigenvalues of an operator A and its powers. As an application, we show that the commutant of an operator A coincides with that of An, n ≥ 2, n ∈ N if the extended point spectrum of A does not contain any n–th root of unity other than 1. The converse is also true if either A or A* has trivial kernel. 相似文献
6.
Let A be a unital C*-algebra with non-zero socle (soc(A)). We introduce the essential conorm of an element a in A (denoted by γ
e
(a)), as the conorm of the element π(a), where π denotes the canonical projection of A onto . It is established that for every von Neumann regular element , γ
e
(a) = max . We characterize the continuity points of the conorm and essential conorm for extremally rich C*-algebras. Some formulae for the distance from zero to the generalized spectrum and Atkinson spectrum are also obtained.
Authors partially supported by I+D MEC projects no. MTM2005-02541 and MTM2007-65959, and Junta de Andalucía grants FQM0199
and FQM1215. 相似文献
7.
Harald K. Wimmer 《Integral Equations and Operator Theory》1995,21(3):362-375
The set of all negative-semidefinite solutions of the CAREA
*
X+XA+XBB
*
X–C
*
C=0 is homeomorphic to a well defined set ofA-invariant subspaces provided that the purely imaginary eigenvalues ofA are controllable. Based on that homeomorphism isolated n.s.d. solutions of the CARE are characterized by properties of their kernels.Research supported by Deutsche Forschungsgemeinschaft (Wi 1219/1-1). 相似文献
8.
Let X be a Banach space and let
A be a closed linear operator on
X. It is shown that the abstract Cauchy problem
enjoys maximal regularity in weighted
L
p
-spaces with weights
, where
,
if and only if it has the property of maximal
L
p
-regularity.
Moreover, it is also shown that the derivation operator
admits an
-calculus in weighted
L
p
-spaces.
Received: 26 February 2003 相似文献
9.
Mikhail A. Chebotar Wen-Fong Ke Pjek-Hwee Lee Ruibin Zhang 《Monatshefte für Mathematik》2006,149(2):91-101
Let R be a ring, A = M
n
(R) and θ: A → A a surjective additive map preserving zero Jordan products, i.e. if x,y ∈ A are such that xy + yx = 0, then θ(x)θ(y) + θ(y)θ(x) = 0. In this paper, we show that if R contains
and n ≥ 4, then θ = λϕ, where λ = θ(1) is a central element of A and ϕ: A → A is a Jordan homomorphism.
The third author is Corresponding author. 相似文献
10.
Let B(X) be the algebra of all bounded linear operators on the Banach space X, and let N(X) be the set of nilpotent operators in B(X). Suppose ?:B(X)→B(X) is a surjective map such that A,B∈B(X) satisfy AB∈N(X) if and only if ?(A)?(B)∈N(X). If X is infinite dimensional, then there exists a map f:B(X)→C?{0} such that one of the following holds:
- (a)
- There is a bijective bounded linear or conjugate-linear operator S:X→X such that ? has the form A?S[f(A)A]S-1.
- (b)
- The space X is reflexive, and there exists a bijective bounded linear or conjugate-linear operator S : X′ → X such that ? has the form A ? S[f(A)A′]S−1.
11.
LetA be the generator of a cosine functionC
t
,t R in a Banach spaceX; we shall connect the existence and uniqueness of aT-periodic mild solution of the equationu = Au + f with the spectral property 1 (C
T
) and, in caseX is a Hilbert space, also with spectral properties ofA.
This research was supported in part by DAAD, West Germany. 相似文献
12.
Convergence of the efficient sets 总被引:2,自引:0,他引:2
LetA
n,n=1, 2, ... be nonempty subsets of a linear metric spaceE andC
n, n=1, 2, ... convex cones ofE. We consider the efficient sets Min(A
n, Cn) and the aim of this paper is to show that under suitable conditions, the convergence ofA
n andC
n toA andC respectively, implies the convergence of Min(A
n,C
n) to Min(A, C). Several illustrative examples are given which clarify the results. 相似文献
13.
LetX be a Banach space and 1p<. LetL be a bounded linear operator fromL
p
([–1,0],X) intoX. Consider the delay differential equationu(t)=Lu
t
,u(0)=x,u
0=f on the state spaceL
p
([–1,0],X). We prove that a mild solutionu(t)=u(t;x,f) is a small solution if and only if the Laplace transform ofu(t;x,f) extends to an entire function. The same result holds for the state spaceC([–1,0],X).This paper was written while the authors were affiliated with the University of Tübingen. It is part of a research project supported by the Deutsche Forschungsgemeinschaft DFG. The authors warmly thank Professor Rainer Nagel and the AG Funktionalanalysis for the stimulating and enjoyable working environment.Support by DAAD is gratefully acknowledged.Support by an Individual Fellowship from the Human Capital and Mobility programme of the European Community is gratefully acknowledged. 相似文献
14.
Ioan I. Vrabie 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7047-7060
In this paper, we prove a sufficient condition for the global existence of bounded C0-solutions for a class of nonlinear functional differential evolution equation of the form where X is a real Banach space, A is the infinitesimal generator of a nonlinear compact semigroup, is a nonempty, convex, weakly compact valued, and almost strongly–weakly u.s.c. multi-function, and is nonexpansive. 相似文献
15.
B. P. Duggal 《Integral Equations and Operator Theory》1996,26(3):338-345
IfA
i
i=1, 2 are quasi-similarp-hyponormal operators such thatUi is unitary in the polar decompositionA
i
=U
i
|A
i
|, then (A
1)=(A
2) and
c(A1) = e(A2). Also a Putnam-Fuglede type commutativity theorem holds for p-hyponomral operators. 相似文献
16.
Aleksander Ćwiszewski 《Journal of Evolution Equations》2007,7(1):1-33
In the paper a topological degree is constructed for the class of maps of the form − A + F where M is a closed neighborhood retract in a Banach space
is a m-accretive map such that − A generates a compact semigroup and F : M→ E is a locally Lipschitz map. The obtained degree is applied to studying the existence and branching of periodic points of
differential inclusions of the type
相似文献
17.
Summary LetA be a closed linear operator on a Banach spaceX. In this work we present some interpolation and extrapolation results for the well posed abstract Cauchy problem of second order; namely, if the second order abstract Cauchy problem is exponentially well posed onD(A
k + 1
),k N thenA is sandwiched by cosine function generators. 相似文献
18.
Bhagwati Prashad Duggal Slavisa V. Djordjević 《Mediterranean Journal of Mathematics》2005,2(4):395-406
It is known that if
and
are Banach space operators with the single-valued extension property, SVEP, then the matrix operator
has SVEP for every operator
and hence obeys Browder’s theorem. This paper considers conditions on operators A, B, and M0 ensuring Weyls theorem for operators MC. 相似文献
19.
We present second-order subdifferentials of Clarke's type of C
1,1 functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in
n
, considered by J. B. H.-Urruty, J. J. Strodiot and V. H. Nguyen. Various properties of these subdifferentials are proved. Second-order optimality conditions (necessary, sufficient) for constrained minimization problems with C
1,1 data are obtained.This work was partially supported by the National Foundation for Scientific Investigations in Bulgaria under contract No. MM-406/1994. 相似文献
20.
Vincent Cachia Hagen Neidhardt Valentin A. Zagrebnov 《Integral Equations and Operator Theory》2002,42(4):425-448
LetA be a positive self-adjoint operator and letB be anm-accretive operator which isA-small with a relative bound less than one. LetH=A+B, thenH is well-defined on dom(H)=dom(A) andm-accretive. IfB is a strictlym-accretive operator obeying
then for the Trotter product formula we prove that
(and similar forH
*) asn, uniformly int0. We also show that: (a) theA-smallness ofB guarantees the condition (1) for (0,1/2), i.e. the estimate (2) holds for (0,1/2); (b) ifB is strictlym-sectorial, then there are sufficient conditions ensuring the relation (1) for =1/2, that implies (2); (c) ifB isA-small,m-sectorial and such that dom(A
1/2) is a subset of the formdomain ofB, then again (2) is valid for =1/2. 相似文献
((1)) |
((2)) |