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1.
The Fuglede-Putnam theorem (in Moore's asymptotic form) on the commutators of normal operators of a Hilbert space is generalized, in particular, in the following form. Leta
1,a
1, b1 and b2 be the elements of a complex Banach algebra such that [a
1 b1]=[a
2, b2]=0 and
as . Then the inequality b
1
x–xb
2(a
1
x–xa
2), where () as 0, holds uniformly in every ball xR<.Translated from Matematicheskie Zametki, Vol. 22, No. 2, pp. 179–188, August, 1977. 相似文献
2.
In this paper we first show that if X is a Banach space and is a left invariant crossnorm on lX, then there is a Banach lattice L and an isometric embedding J of X into L, so that I J becomes an isometry of lX onto lm J(X). Here I denotes the identity operator on l and lm J(X) the canonical lattice tensor product. This result is originally due to G. Pisier (unpublished), but our proof is different. We then use this to prove the main results which characterize the Gordon–Lewis property GL and related structures in terms of embeddings into Banach lattices. 相似文献
3.
The main results obtained are:– A Dedekind complete Banach lattice Y has a Fatou norm if and only if, for any Banach lattice X, the regular-norm unit ball Ur = {T Lr(X,Y): ||T||r 1} is closed in the strong operator topology on the space of all regular operators, Lr(X,Y).– A Dedekind complete Banach lattice Y has a norm which is both Fatou and Levi if and only if, for any Banach lattice X, the regular-norm unit ball Ur is closed in the strong operator topology on the space of all bounded operators, L(X,Y).– A Banach lattice Y has a Fatou–Levi norm if and only if for every L-space X the space L(X,Y) is a Banach lattice under the operator norm.– A Banach lattice Y is isometrically order isomorphic to C(S) with the supremum norm, for some Stonean space S, if and only if, for every Banach lattice X, L(X,Y) is a Banach lattice under the operator norm.Several examples demonstrating that the hypotheses may not be removed, as well as some applications of the results obtained to the spaces of operators are also given. For instance:– If X = Lp() and Y = Lq(), where 1 < p,q < , then Lr(X,Y) is a first category subset of L(X,Y). 相似文献
4.
On the Fell topology 总被引:3,自引:0,他引:3
Gerald Beer 《Set-Valued Analysis》1993,1(1):69-80
Let 2
X
denote the closed subsets of a Hausdorff topological space <X, {gt}>. The Fell topology F on 2
X
has as a subbase all sets of the form {A 2
X
:A V 0}, whereV is an open subset ofX, plus all sets of the form {A 2
X
:A W}, whereW has compact complement. The purpose of this article is two-fold. First, we characterize first and second countability for F in terms of topological properties for . Second, we show that convergence of nets of closed sets with respect to the Fell topology parallels Attouch-Wets convergence for nets of closed subsets in a metric space. This approach to set convergence is highly tractable and is well-suited for applications. In particular, we characterize Fell convergence of nets of lower semicontinuous functions as identified with their epigraphs in terms of the convergence of sublevel sets. 相似文献
5.
A fluid model with infinite buffer is considered. The total net rate is a stationary Gaussian process with mean –c and covariance functionR(t). Let (x) be the probability that in steady state conditions the buffer content exceedsx. Under the condition
0
t
2 ¦R(t)¦dt< we show that admits a logarithmic linear upper bound, i.e. (x)Cexp[–x]+o(exp[–x]) and find and C. Special cases are worked out whenR is as in a Gauss-Markov or AR-Gaussian process. 相似文献
6.
Noboru Hamada 《Graphs and Combinatorics》1989,5(1):137-147
Recently, Hamada [5] characterized all {v
2 + 2v
1,v
1 + 2v
0;t,q}-min · hypers for any integert 2 and any prime powerq 3 wherev
l
= (q
l – 1)/(q – 1) for any integerl 0. The purpose of this paper is to characterize all {v
+ 1 + 2v
,v
+ 2v
– 1;t,q}-min · hypers for any integerst, and any prime powerq such thatt 3, 2 t – 1 andq 5 and to characterize all (n, k, d; q)-codes meeting the Griesmer bound (1.1) for the casek 3, d = q
k-1 – (2q
-1 +q
) andq 5 using the results in Hamada [3, 4, 5]. 相似文献
7.
We consider a functional differential equation (1) (t)=F(t,) fort[0,+) together with a generalized Nicoletti condition (2)H()=. The functionF: [0,+)×C
0[0,+)B is given (whereB denotes the Banach space) and the value ofF (t, ) may depend on the values of (t) fort[0,+);H: C
0[0,+)B is a given linear operator and B. Under suitable assumptions we show that when the solution :[0,+)B satisfies a certain growth condition, then there exists exactly one solution of the problem (1), (2). 相似文献
8.
We prove that E is a p-fine domain whenever R
n
is a p-fine domain, E R
n
is p-polar, and 1 < p n. By a p-fine domain we understand an open connected set in the p-fine topology, i.e. in the coarsest topology making all p-superharmonic functions continuous. As an application of our main result, we establish a general version of minimum principle. 相似文献
9.
In the present paper we consider a selfadjoint and nonsmooth operator-valued function on (c, d)R
1. We suppose that the equation (L()x, x)=0,x0, has exactly one rootp(x) (c, d) and the functionf()=(L()x, x) is increasing at the pointp(x). We discuss questions of the variational theory of the spectrum. Some theorems on the variational properties of the spectrum are proved. 相似文献
10.
Summary For each in some domainD in the complex plane, letF() be a linear, compact operator on a Banach spaceX and letF be holomorphic in . Assuming that there is a so thatI–F() is not one-to-one, we examine two local methods for approximating the nonlinear eigenvalue . In the Newton method the smallest eigenvalue of the operator pencil [I–F(),F()] is used as increment. We show that under suitable hypotheses the sequence of Newton iterates is locally, quadratically convergent. Second, suppose 0 is an eigenvalue of the operator pencil [I–F(),I] with algebraic multiplicitym. For fixed leth() denote the arithmetic mean of them eigenvalues of the pencil [I–F(),I] which are closest to 0. Thenh is holomorphic in a neighborhood of andh()=0. Under suitable hypotheses the classical Muller's method applied toh converges locally with order approximately 1.84. 相似文献
11.
Paul Günther 《Annals of Global Analysis and Geometry》1994,12(1):219-236
LetM
t[](x) be the spherical mean value operator applied to a function on a symmetric Riemannian space of the non-compact type.L
—decay estimations forM
t
[](x) as well as for its derivatives with respect to (t, x) are given, provided that belongs to a Banach space with suitable weighted supremum norm. This leads to estimates of the solutions to the wave equation in certain cases in which Huygens' principle is valid. 相似文献
12.
Dana D. Clahane 《Integral Equations and Operator Theory》2005,51(1):41-56
Let H2(D) denote the Hardy space of a bounded symmetric domain
in its standard Harish-Chandra realization, and let
be the weighted Bergman space with
and
where
is a critical value depending on D. Suppose that
is holomorphic. We show that if the composition operator
defined by
is compact (or, more generally, power-compact) on H2(D) or
then has a unique fixed point z0 in D. We then prove that the spectrum of
as an operator on these function spaces is precisely the set consisting of 0, 1, and all possible products of eigenvalues of
These results extend previous work by Caughran/Schwartz and MacCluer. As a corollary, we now have that MacCluers previous spectrum results on the unit ball Bn extend to Hp(n) (not only for p = 2 but for all p > 1) and
(for p 1), where n is the polydisk in
相似文献
13.
V. M. Petrichkovich 《Journal of Mathematical Sciences》1999,96(2):3022-3025
We describe all the factorizations A=BC (up to associates) of a matrix A over a commutative principal ideal domain parallel to the factorization DA= of its canonical diagonal form DA ( and are diagonal matrices), that is, the factorizations such that the matrices B and C are equivalent to the matrices and respectively.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 96–100. 相似文献
14.
A. F. Vakulenko 《Journal of Mathematical Sciences》1984,27(2):2559-2561
One considers a self-adjoint operator H for which one has a unitary group U such that the operator H UHU
–1
is analytic with respect to . Under certain additional restrictions on H, one proves the absence of the singular continuous spectrum of H. In this connection one admits such a behavior of the essential spectrum of H for Im 0 which excludes the application of the method of analytic dilatations. In our analysis, analogies with the method of the inverse scattering problem play an important role.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 127, pp. 3–6, 1983. 相似文献
15.
Aarni Lehtinen 《Mathematical Methods of Operations Research》1993,37(1):97-106
The secretary problem with a known prior distribution of the number of candidates is considered. Ifp(i)=p(N=i),i [, ] , where=inf{i :p(i) > 0} and=sup{i :p(i)0}, is the prior distribution of the numberN of candidates it will be shown that, if the optimal stopping rule is of the simple form, then the optimal stopping indexj=min satisfies asymptotically (as ) the equationj=exp
.The probability of selecting the best object by the corresponding policy will be (j-1)
p(i)/i. We also give an example of the distributionp for which the optimal stopping rule consists of a stopping set with two islands. We present an asymptotical solution for this example. 相似文献
16.
In this paper we study the positive resolvent values of positive operators respectively of positive elements in Banach lattice ordered algebras. In the matrix case these values are just the inverse M-matrices. One of the main results is the following: Let A be a Banach lattice ordered algebra. A positive invertible element xA is a resolvent value of a positive element yA if and only if the element x satisfies the negative principle: If aA, < 0 and xaa then xa 0. 相似文献
17.
Convergence rates of Newton-Goldstein sequences are estimated for convex constrained minimization problems with singular solutions, i.e., solutions at which the local quadratic approximationQ(, x) to the objective functionF grows more slowly than x – 2 for admissible vectorsx near. For a large class of iterative minimization methods with quadratic subproblems, it is shown that the valuesr
n
=F(x
n
)–inf
F are of orderO(n
–1/3) at least. For the Newton—Goldstein method this estimate is sharpened slightly tor
n
=O(n
–1/2) when the second Fréchet differentialF is Lipschitz continuous and the admissible set is bounded. Still sharper estimates are derived when certain growth conditions are satisfied byF or its local linear approximation at. The most surprising conclusion is that Newton—Goldstein sequences can convergesuperlinearly to a singular extremal whenF(), x – Ax –
v
for someA > 0, somev (2,2.5) and allx in near, and that this growth condition onF() is entirely natural for a nontrivial class of constrained minimization problems on feasible sets =
1{[0,1],U} withU a uniformly convex set in
d
. Feasible sets of this kind are commonly encountered in the optimal control of continuous-time dynamical systems governed by differential equations, and may be viewed as infinite-dimensional limits of Cartesian product setsU
k
in
kd
. Superlinear convergence of Newton—Goldstein sequences for the problem (,F) suggests that analogous sequences for increasingly refined finite-dimensional approximation (U
kd
,F
k
) to (,F) will exhibit convergence properties that are in some sense uniformly good ink ask .Investigation partially supported by the U.S. Air Force through the Air Force Institute of Technology, and by NSF Grant ECS-8005958. 相似文献
18.
Given a bounded linear operatorA in an infinite dimensional Banach space and a compact subset of a connected component of its semi-Fredholm domain, we construct a finite rank operatorF such that –A+F is bounded below (or surjective) for each ,F
2=0 and rankF=max min{dimN(–A), codimR(–A)}, if ind(–A)0 (or ind(–A)0, respectively) for each . 相似文献
19.
E. D. Rogak N. D. Kazarinoff J. F. Scott-Thomas 《Journal of Optimization Theory and Applications》1970,5(1):1-11
Sufficient conditions for bang-bang and singular optimal control are established in the case of linear operator equations with cost functionals which are the sum of linear and quadratic terms, that is,Ax=u,J(u)=(r,x)+(x,x), >0. For example, ifA is a bounded operator with a bounded inverse from a Hilbert spaceH into itself and the control setU is the unit ball inH, then an optimal control is bang-bang (has norm l) if 0<1/2;A
–1*r·A
–1–2, but is singular (an interior point ofU) if >1/2A
–1*r·A2.This work was supported by NRC Grant No. A-4047 and NSF Grant No. GP-7445. 相似文献
20.
Joanna Janczewska 《Geometriae Dedicata》2002,91(1):7-21
The aim of this paper is to illustrate the use of topological degree for the study of bifurcation in von Kármán equations with two real positive parameters and for a thin elastic disk lying on the elastic base under the action of a compressing force, which may be written in the form of an operator equation F(x, , ) = 0 in some real Banach spaces X and Y. The bifurcation problem that we study is a mathematical model for a certain physical phenomenon and it is very important in the mechanics of elastic constructions. We reduce the bifurcation problem in the solution set of equation F(x, , ) = 0 at a point (0, 0, 0) X × IR
+
2 to the bifurcation problem in the solution set of a certain equation in IR
n
at a point (0, 0, 0) IR
n
× IR
+
2, where n = dim Ker F
x
(0, 0, 0) and F
x
(0, 0, 0): X Y is a Fréchet derivative of F with respect to x at (0, 0, 0). To solve the bifurcation problem obtained as a result of reduction, we apply homotopy and degree theory. 相似文献