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1.
We consider a selfadjoint and smooth enough operator-valued functionL() on the segment [a, b]. LetL(a)0,L(b)0, and there exist two positive numbers and such that the inequality |(L()f, f)|< ([a, b] f=1) implies the inequality (L'()f, f)>. Then the functionL() admits a factorizationL()=M()(I-Z) whereM() is a continuous and invertible on [a, b] operator-valued function, and operatorZ is similar to a selfadjoint one. This result was obtained in the first part of the present paper [10] under a stronge conditionL()0 ( [a,b]). For analytic functionL() the result of this paper was obtained in [13]. 相似文献
2.
LetT B(H) be a bounded linear operator on a complex Hilbert spaceH. Let 0 (T) be an isolated point of (T) and let
be the Riesz idempotent for 0. In this paper, we prove that ifT isp-hyponormal or log-hyponormal, thenE is self-adjoint andE
H=ker(H–0)=ker(H–0
*.This research was supported by Grant-in-Aid Research 1 No. 12640187. 相似文献
3.
In this paper we find a relation between the lattice of hyperinvariant subspaces of an operatorT of classC
0 over a multiply connected region and that of its Jordan modelT. It is shown that, generally, the lattice corresponding toT can be identified with a retract of that corresponding toT. Thus the Jordan model has the smallest lattice of hyperinvariant subspaces in a given quasisimilarity class. 相似文献
4.
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
5.
A spatially nonhomogeneous random walk t on the grid =m X n is considered. Let t
0 be a random walk homogeneous in time and space, and let t be obtained from it by changing transition probabilities on the set A= X n, || < , so that the walk remains homogeneous only with respect to the subgroup n of the group . It is shown that if >m 2 or the drift is distinct from zero, then the central limit theorem holds for t. 相似文献
6.
In this paper, we show that ifT is a -hyponormal operator, thenT
2 is also -hyponormal. 相似文献
7.
Yin Chen 《Integral Equations and Operator Theory》2001,41(3):255-263
Let (E
0,E
1) be a compatible couple of Banach spaces, and letE
: 0Re1 be the complex interpolation spaces ofE
0,E
1. LetT be a closed linear operator onE
0+E
1, then the restrictionT
ofT to eachE
is closed. If we denote by
the extended spectrum ofT
inE
, then, under appropriate conditions, it is shown that the map
is an analytic multifunction in the strip {C0<Re<1}. We use these results to give some applications to the spectral theory of semigroups. 相似文献
8.
Roland Wolff 《Integral Equations and Operator Theory》2000,38(1):120-127
In this paper, we prove that the Hardy spaceH
p
(), 1p<, over a strictly pseudoconvex domain in
n
with smooth boundary is quasi-coherent. More precisely, we show that Toeplitz tuplesT
with suitable symbols onH
p
() have property (). This proof is based on a well known exactness result for the tangential Cauchy-Riemann complex. 相似文献
9.
The strongly irreducible operators in nest algebras 总被引:2,自引:0,他引:2
An operatorT on
is called strongly irreducible ifT does not commute with any nontrivial idempotent operator. In this paper, we first show that each nest algebra (
) has strongly irreducible operators. Secondly, we obtain a characterization of operators which can be uniquely written as a direct sum of finitely many strongly irreducible operators. Finally, we characterize the strongly irreducibility of operators in a nest algebra (
).This project was partially supported by National Natural Science Foundation of China. 相似文献
10.
T. I. Akhobadze 《Analysis Mathematica》1982,8(2):79-102
. , , –1<<0. .
The present work was written on the basis of two earlier works received byAnalysis Mathematica on January 16, 1979, and July 20, 1979. 相似文献
The present work was written on the basis of two earlier works received byAnalysis Mathematica on January 16, 1979, and July 20, 1979. 相似文献
11.
We consider the family {X
, 0} of solution to the heat equation on [0,T]×[0,1] perturbed by a small space-time white noise, that is
t
X
=
X
+b({X
})+({X
})
. Then, for a large class of Borelian subsets of the continuous functions on [0,T]×[0,1], we get an asymptotic expansion of P({X
}A) as 0. This kind of expansion has been handled for several stochastic systems, ranging from Wiener integrals to diffusion processes. 相似文献
12.
Self-adjoint quadratic operator pencilsL()=
2
A + B + C with a noninvertible leading operatorA are considered. In particular, a characterization of the spectral points of positive and of negative type ofL is given, and their behavior under a compact perturbation is studied. These results are applied to a pencil arising in magnetohydrodynamics. 相似文献
13.
Converse theorems for multidimensional Kantorovich operators 总被引:4,自引:0,他引:4
Ding -Xuan Zhou 《Analysis Mathematica》1993,19(1):85-100
L
p
[0, l]. . . - .
Supported by National Science Foundation, Zhejiang Provincial Science Foundation of China, and Alexander von Humboldt Foundation of Germany. 相似文献
Supported by National Science Foundation, Zhejiang Provincial Science Foundation of China, and Alexander von Humboldt Foundation of Germany. 相似文献
14.
On log-hyponormal operators 总被引:9,自引:0,他引:9
Kôtarô Tanahashi 《Integral Equations and Operator Theory》1999,34(3):364-372
LetTB(H) be a bounded linear operator on a complex Hilbert spaceH.TB(H) is called a log-hyponormal operator itT is invertible and log (TT
*)log (T
*
T). Since log: (0, )(–,) is operator monotone, for 0<p1, every invertiblep-hyponormal operatorT, i.e., (TT
*)
p
(T
*
T)
p
, is log-hyponormal. LetT be a log-hyponormal operator with a polar decompositionT=U|T|. In this paper, we show that the Aluthge transform
is
. Moreover, ifmeas ((T))=0, thenT is normal. Also, we make a log-hyponormal operator which is notp-hyponormal for any 0<p.This research was supported by Grant-in-Aid Research No. 10640185 相似文献
15.
J. Globevnik 《Monatshefte für Mathematik》1980,90(3):195-205
LetK be a compact Hausdorff space and letFK be a peak interpolation set for a function algebraAC(K). Let be a map fromK to the family of all convex subsets of such that the set {(z, x)zK, x(z)} is open inK×C and such thatg(z)(z) (zK) for somegA. We prove that everyfC(F) satisfyingf(s)(s) (sF) (f(s)closure (s) (sF)) admits an extensionfAA} satisfyingf(z)(z) (zK) (f(z))}closure (z) (zK), respectively). We prove a more general theorem of this kind and present various applications which generalize known dominated interpolation theorems for subspaces ofC(K). 相似文献
16.
17.
Péter Komjáth 《Analysis Mathematica》1984,10(4):283-293
. , A
0,A
1,— - lim supA
j
- H,
. , - - . , , ; , , . - . - . 相似文献
18.
R. Ž. Nurpeisov 《Analysis Mathematica》1989,15(2):127-143
H
(G), f(g)H
(G) , (, 1)- OHMC G. , OHMC, A. H. . , . , OHMC, lim supp
n=, , ,n .. . , 117 234 . . - 相似文献
19.
Letp(1, ). In this paper, the authors investigate the uniformL
p
(
n
) in of the oscillatory singular integral operatorT
defined by
where , is a real analytic function or a real-C
function on
n
×
n
, C
0
(
n
×
n
) andk is a variable Calderón-Zygmund kernel. Moreover, the uniform boundedness in of the commutators generated byT
and BMO(
n
) functions onL
p
(
n
) is also obtained.The research is supported in part by the NNSF and the SEDF of China. 相似文献
20.
We give a new2 index theorem for the basic example of Toeplitz operators on the circle. The joint torsion, a non zero complex valued analytic index, of a pair of Fredholm Toeplitz operatorsT
andT
withH
symbols is computed by residues in the disk, and is determined by a monodromy integral which specifies the isomorphism class of a flat line bundle on the circle. When the symbols and are rational a product of joint torsions identifies the isomorphism class of the bundle inH
1 (S
1,C
*), and the identification extends by rational approximation to the case of smooth symbols defined on the circle.Partially supported by National Science Foundation grants to both authors. 相似文献