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1.
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
2.
— [0,1] ,E — - e=1 [0,1]. I —
E
=1, E=L
2 x
e
=xL
2 x E.
This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund. 相似文献
This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund. 相似文献
3.
4.
LetE be a Dedekind complete complex Banach lattice and letD denote the diagonal projection from the spaceL
r
(E) onto the centerZ(E) ofE. Let {T(t)}
t0 be a positive strongly continuous semigroup of linear operators with generatorA. The first main result is that if the spectral bounds(A) equals to zero, then the functionD(T(t)) is a center valuedp-function. The second main result is that if for >0 the diagonalD(R(, A)) of the resolvent operatorR(, A) is strictly positive, then (D(R(, A)))
–1 is a center valued Bernstein function. As an application of these results it follows that the order limit lim0D(R(,A)) exists inZ(E) and equals the order limit lim
m
D((R(, A))
m
) for any >0. 相似文献
5.
We show that for any simple piecewise Ljapunov contour there exists a power weight such that the essential norm |S
| in the spaceL
2(, ) does not depend on the angles of the contour and it is given by formula (2). All such weights are described. For the union =12 of two simple piecewise Lyapunov curves we prove that the essential norm |S
| inL
2() is minimal if both 1 and 2 are smooth in some neighborhoods of the common points. It is the case when the norm |S
| in the spaceL
2() as well as inL
2(, ) does not depend on the values of the angles and it can be calculated by formula (5). 相似文献
6.
G. G. Gevorkyan 《Analysis Mathematica》1986,12(3):185-190
, (t) >0 E(–, +),E<, , ¦f(t)¦ (t)
xE, f(t)=0 (–, +). 相似文献
7.
8.
В. Н. Деменко 《Analysis Mathematica》1989,15(1):17-35
p- . E R
n -, f () p(R
n)., ER
n 2nq
0, E— - q
0(q
0-1). : q0>2 n1 E
R
n 2nq
0, p- p<0. , f-[-, ]n, f A
p(R
n) ,
p([-, ]n) (1 << ). 相似文献
9.
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
10.
D. V. Leladze 《Analysis Mathematica》1991,17(4):281-295
n- (n1) fL
p
([–, ]
n
),=1 = (L
C) . , , f([–, ]
n
). 相似文献
11.
Thorsten Kröncke 《Integral Equations and Operator Theory》2001,40(1):80-105
Let T- S, be a family of not necessarily bounded semi-Fredholm operators, where T and S are operators acting between Banach spaces X and Y, and where S is bounded with D(S) D(T). For compact sets , as well as for certain open sets , we investigate existence and minimal rank of bounded feedback perturbations of the form F=BE such that min.ind (T-S+F)=0 for all . Here B is a given operator from a linear space Z to Y and E is some operator from X to Z.We give a simple characterization of that situation, when such regularizing feedback perturbations exist and show that for compact sets the minimal rank never exceeds max { min.ind (T-S) }+1. Moreover, an example shows that the minimal rank, in fact, may increase from max {...} to max {...}+1, if the given B enforces a certain structure of the feedbachk perturbation F.However, the minimal rank is equal to max { min.ind (T-S) }, if is an open set such that min.ind (T-S) already vanishes for all but finitely many points . We illustrate this result by applying it to the stabilization of certain infinite-dimensional dynamical systems in Hilbert space. 相似文献
12.
V. A. Andrienko 《Analysis Mathematica》1996,22(4):243-266
( ) . .
Dedicated to Professor K. Tandori on his seventieth birthday
This research was supported in part by Grant # K41 100 of the Joint Fund of the Government of Ukraine and the International Science Foundation. 相似文献
Dedicated to Professor K. Tandori on his seventieth birthday
This research was supported in part by Grant # K41 100 of the Joint Fund of the Government of Ukraine and the International Science Foundation. 相似文献
13.
Victor Kaftal 《Integral Equations and Operator Theory》1982,5(1):50-70
LetA be a von Neumann algebra,J be the ideal of compact operators relative toA and letF
+ be the left-Fredholm class ofA. We call almost left-Fredholm the class
= {A A: if P A is a projection and AP J then P J}. Then
and the inclusion is proper unlessA is semifinite and has a non-large center.
satisfies all of the algebraic properties ofF
+ but it is generally not open. IfA is semifinite then A
iff there are central projectionsG
with G = I such that AG F+(AG). Let :A A/J. Then the left almost essential spectrum ofA A,
, coincides with the set of eigenvalues of (A) 相似文献
14.
F. Schipp 《Analysis Mathematica》1990,16(2):135-141
H={h
1,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H
={h
(I),I} . , , . L
p
.
Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday
This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153. 相似文献
Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday
This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153. 相似文献
15.
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
16.
We construct dense sets of hypercyclic vectors for unbounded differention operators, including differentiation operators on the Hardy spaceH
2, and the Laplacian operator onL
2((), for any bounded open subset of 2. Furthermore, we show that these operators are chaotic, in the sense of Devaney. 相似文献
17.
Compact and weakly compact weighted composition operators on weighted spaces of continuous functions
In this note we characterize the compact and weakly compact weighted composition operatorsW
, on certain weighted locally convex spacesCV
o(X, E) of vector-valued continuous functions induced by self maps ofX and the operator-valued mappings XB(E).The work of this author was supported in part by CSIR Grant 9/100/92-EMR-IThe work of this author was supported in part by UGC Grant F.8-7/91 (RBB-II) 相似文献
18.
V. F. Gapoškin 《Analysis Mathematica》1980,6(2):105-119
a
k
f
k
, f
k
L
2, w-, (2), w(n) — .
a
k
f
k
N {a
k
}l
2, {a
k
}l
2 ( 1, 2, 1a, 2a). ( 2) [8]. , {a
k
} w-. 相似文献
19.
1<q<2 L:=
n=1
1/q
n=1/q–1. [0,1]
n()=1, A
n:=
i=1
n–1
i(x)/qi+1/n
x
n(x)=0, n>. , =
n=1
n(x)/qn. F: [0,L]R , F(x)=
n=1
n(x)an,
n=1
¦a
n¦<. [0,L]. q(1,2), . , q(1, 2), . . 相似文献
20.
J. Lippus 《Analysis Mathematica》1984,10(3):213-231
- ()N2,L
F
(
) — , 2- , {s
m()
f} -L.
— . (L
F(
),L
F(
) ={(k)} (kZ2) , fLF(
) f
,
, L
F(
). - ={()} ={()} , n(())m()n(()+())
. R() , ..
- . , . (L
F
(
),L
F
(
)) , R(,)=O(1) (x).
The author wishes to express his gratitude to S. A.Teljakovski for setting the problem and for his attention to this paper. 相似文献
The author wishes to express his gratitude to S. A.Teljakovski for setting the problem and for his attention to this paper. 相似文献