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1.
To an evolution family on the half-line
of bounded operators on a Banach space X we associate operators IX and IZ related
to the integral equation
and a closed
subspace Z of X. We characterize the exponential dichotomy of
by the
exponential dichotomy and the quasi-exponential dichotomy of the operators
X we associate operators IX and IZ, respectively. 相似文献
2.
O. V. Sarafanov 《Journal of Mathematical Sciences》2004,120(2):1195-1239
The C
*-algebra
generated by the operators of pseudodifferential boundary value problems on a manifold
with smooth closed disjoint edges and boundary
is studied. The operators act in the space L
2(
)
L
2(
). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra
Bibliography: 12 titles. 相似文献
3.
Daoxing Xia 《Integral Equations and Operator Theory》1999,33(4):489-506
This paper studies the class of pure operatorsA on a Hilbert space
satisfying dimK
A
<, where
. The main tool is a pair of matrices
and
. A reproducing kernel Hilbert space model is introduced for a subclass of this class of operators. Some theorems are established for some subnormal operators as well as hyponormal operators in this class. 相似文献
4.
In 1997, V. Pták defined the notion of generalized Hankel operator as follows: Given two contractions
and
, an operatorX:
is said to be a generalized Hankel operator ifT
2
X=XT
1
*
andX satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations ofT
1 andT
2. The purpose behind this kind of generalization is to study which properties of classical Hankel operators depend on their characteristic intertwining relation rather than on the theory of analytic functions. Following this spirit, we give appropriate versions of a number of results about compact and finite rank Hankel operators that hold within Pták's generalized framework. Namely, we extend Adamyan, Arov and Krein's estimates of the essential norm of a Hankel operator, Hartman's characterization of compact Hankel operators and Kronecker's characterization of finite rank Hankel operators.Dedicated to the memory of our master and friend Vlastimil Pták 相似文献
5.
Let M be a smooth manifold,
the space of polynomial on fibers functions on T*M (i.e., of symmetric contravariant tensor fields). We compute the first cohomology space of the Lie algebra, Vect(M), of vector fields on M with coefficients in the space of linear differential operators on
. This cohomology space is closely related to the Vect(M)-modules,
(M), of linear differential operators on the space of tensor densities on M of degree . 相似文献
6.
In this note we study some properties concerning certain copies of the classic Banach space c
0 in the Banach space
of all bounded linear operators between a normed space X and a Banach space Y equipped with the norm of the uniform convergence of operators. 相似文献
7.
We discuss purely singular finite-rank perturbations of a self-adjoint operator A in a Hilbert space . The perturbed operators
are defined by the Krein resolvent formula
, Im z 0, where B
z are finite-rank operators such that dom B
z dom A = |0}. For an arbitrary system of orthonormal vectors
satisfying the condition span |
i
} dom A = |0} and an arbitrary collection of real numbers
, we construct an operator
that solves the eigenvalue problem
. We prove the uniqueness of
under the condition that rank B
z = n. 相似文献
8.
In this paper we show that the theory of Hankel operators in the torus
d
, ford>1, presents striking differences with that on the circle
, starting with bounded Hankel operators with no bounded symbols. Such differences are circumvented here by replacing the space of symbolsL
(
) by BMOr(
d
), a subspace of product BMO, and the singular numbers of Hankel operators by so-called sigma numbers. This leads to versions of the Nehari-AAK and Kronecker theorems, and provides conditions for the existence of solutions of product Pick problems through finite Picktype matrices. We give geometric and duality characterizations of BMOr, and of a subspace of it, bmo, closely linked withA
2 weights. This completes some aspects of the theory of BMO in product spaces.Sadosky was partially supported by NSF grants DMS-9205926, INT-9204043 and GER-9550373, and her visit to MSRI is supported by NSF grant DMS-9022140 to MSRI. 相似文献
9.
Aleksandar Torgašev 《Czechoslovak Mathematical Journal》1998,48(1):77-83
Let B(X) be the algebra of all bounded linear operators in a complex Banach space X. We consider operators T
1, T
2 B(X) satisfying the relation
for any vector x X, where
T
(x) denotes the local spectrum of T B(X) at the point x X. We say then that T
1 and T
2 have the same local spectra. We prove that then, under some conditions, T
1 – T
2 is a quasinilpotent operator, that is
as n . Without these conditions, we describe the operators with the same local spectra only in some particular cases. 相似文献
10.
In this paper we show how wavelets originating from multiresolution analysis of scaleN give rise to certain representations of the Cuntz algebrasO
N
, and conversely how the wavelets can be recovered from these representations. The representations are given on the Hilbert space
by (S
i
) (z)=m
i
(z)(z
N
). We characterize the Wold decomposition of such operators. If the operators come from wavelets they are shifts, and this can be used to realize the representation on a certain Hardy space over
. This is used to compare the usual scale-2 theory of wavelets with the scale-N theory. Also some other representations ofO
N
of the above form called diagonal representations are characterized and classified up to unitary equivalence by a homological invariant.Work supproted in part by the U.S. National Science Foundation and the Norwegian Research Council. 相似文献
11.
In 1997 Ptak defined generalized Hankel operators as follows: Given two contractions
and
, an operator
is said to be a generalized Hankel operator if
and X satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of T
1 and T
2. This approach, call it (P), contrasts with a previous one developed by Ptak and Vrbova in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong but somewhat hidden connection between the theories (P) and (PV) and we clarify that connection by proving that (P) is more general than (PV), even strictly more general for some T
1 and T
2, and by studying when they coincide. Then we characterize the existence of Hankel operators, Hankel symbols and analytic Hankel symbols, solving in this way some open problems proposed by Ptak. 相似文献
12.
Semi-commutators of Toeplitz operators on the Bergman space 总被引:3,自引:0,他引:3
Dechao Zheng 《Integral Equations and Operator Theory》1996,25(3):347-372
In this paper several necessary and sufficient conditions are obtained for the semi-commutator
of Toeplitz operators
andT
g
with bounded pluriharmonic symbols on the unit ball to be compact on the Bergman space. Using
-harmonic function theory on the unit ball we show that
with bounded pluriharmonic symbolsf andg is zero on the Bergman space of the unit ball or the Hardy space of the unit sphere if and only if eitherf org is holomorphic.The author was supported in part by the National Science Foundation. 相似文献
13.
Let C be the space of 2-periodic continuous functions with uniform norm, let r(f,h) be a modulus of continuity of order r of a function f, and let
Then
for
.An explicit formula for the sum of the series on the right-hand side is derived. Analogs of r(h) also obtained for other spaces, in particular, for the space L. Sharp estimates for a series of convolution operators are obtained in terms of the norm of the second-order derivative of a function, in particular, sharp estimates for the norm of deviation of the Steklov function of order r are derived in terms of the norm of the second-order derivative. Bibliography: 10 titles. 相似文献
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14.
15.
P. M. Akhmet'ev 《Journal of Mathematical Sciences》2004,119(1):5-9
Pairs B,
of divergence-free vector fields with compact support in
are considered higher-order analog M(B,
c (of order 3) of the Gauss helicity number H(B,
)=
, curl(A)=B; (of order 1) is constructed, which is invariant under volume-preserving diffeomorphisms. An integral expression for M is given. A degree-four polynomial m(B(x1), B(x2),
(
1),
(
2)), x1, x2,
1
2
, is defined, which is symmetric in the first and second pairs of variables separately. M is the average value of m over arbitrary configurations of points. Several conjectures clarifying the geometric meaning of the invariant and relating it to invariants of knots and links are stated. Bibliography: 11 titles. 相似文献
16.
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
17.
This paper is devoted to the study of the approximation properties of linear operators which are partial Fourier--Legendre sums of order n with 2r terms of the form
k=1
2r
akPn+k(x) added; here P
m(x) denotes the Legendre polynomial. Due to this addition, the linear operators interpolate functions and their derivatives at the endpoints of the closed interval [-1,1], which, in fact, for r= = 1 allows us to significantly improve the approximation properties of partial Fourier--Legendre sums. It is proved that these operators realize order-best uniform algebraic approximation of the classes of functions
and A
q
(B). With the aim of the computational realization of these operators, we construct their discrete analogs by means of Chebyshev polynomials, orthogonal on a uniform grid, also possessing nice approximation properties. 相似文献
18.
19.
Asao Arai 《Integral Equations and Operator Theory》1993,16(1):38-63
LetA andB be anticommuting self-adjoint operators in a Hilbert space . It is proven thatiAB is essentially self-adjoint on a suitable domain and its closureC(A, B) anticommutes withA andB. LetU
s
be the partial isometry associated with the self-adjoint operatorsS, i.e., the partial isometry defined by the polar decompositionS=U
S
|S|. LetP
S
be the orthogonal projection onto (KerS). Then the following are proven: (i) The operatorsU
A
,U
B
,U
C(A,B)
,P
A
,P
B
, andP
A
P
B
multiplied by some constants satisfy a set of commutation relations, which may be regarded as an extension of that satisfied by the standard basis of the Lie algebra
of the special unitary groupSU(2); (ii) There exists a Lie algebra
associated with those operators; (iii) If is separable andA andB are injective, then
gives a completely reducible representation of
with each irreducible component being the spin representation of the Clifford algebra associated with 3; This result can be extended to the case whereA andB are not necessarily injective. Moreover, some properties ofA+B are discussed. The abstract results are applied to Dirac operators. 相似文献
20.
M. F. Gamal' 《Journal of Mathematical Sciences》2004,120(5):1672-1679
A contraction T acting on a Hilbert space H is called a weak contraction if the spectrum of T does not cover the unit disk
and the operator I-T
*
T is of trace class. Operators T1:H1
H1 and T2:H2
H2 are called quasisimilar if there exist operators >X:H1
H2 and Y:H2
H1 such that T2X=XT1, YT2=T1Y, and X and Y have zero kernels and dense ranges. It is proved that if two weak contractions T1 and T2 acting on separable spaces H1 and H2 are quasisimilar, then there exists an operator X:H1
H2 such that XT1=T2X and the mapping
, where
E=clos XE for E
Lat T1, is a lattice isomorphism. An example is given of two quasisimilar weak contractions such that for any isomorphism
, its inverse is not equal to
for a (bounded) operator Y. Bibliography: 4 titles. 相似文献