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1.
Dominik Mielczarek 《Monatshefte für Mathematik》2008,154(2):157-171
In this paper we will prove that an averaging projection P
a
: K (H) → Y, given by the formula
, is the only norm-one projection. Here, K (H) is a space of compact operators on a separable real Hilbert space H, and Y is the subspace of K(H) consisting of all symmetric operators.
Author’s address: Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków,
Poland 相似文献
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Orthogonality and range closure properties are studied for certain elementary operators derived from hyponormal operators or contractions on a Hilbert space. 相似文献
4.
Let f be a generalized holomorphic function on a connected open set
. It is proved that f equals zero if and only if there exists a smooth curve and a set A of positive (one-dimensional) measure such that f takes zero value on A. Also, a holomorphic generalized function different from zero on the disc, which takes zero values on a dense G
δ-set of the disc, is constructed. The generalized zero set of a holomorphic function is introduced and studied in an analogous
way. 相似文献
5.
Starting from the Colombeau Generalized Functions, the sharp topologies and the notion of generalized points, we introduce a new kind of differential calculus (for functions between totally disconnected spaces). We also define here the notions of holomorphic generalized functions (in this new framework) and generalized manifold. Finally we give an answer to a question raised in [6].Research partially supported by CNPq (Proc 300652/95-0). 相似文献
6.
The structure of the subspaces having the Dunford-Pettis property (DPP) is studied, where is the space of all compact operators on and . The following conditions are shown to be equivalent: (i) M has the DPP, (ii) M is isomorphic to a subspace of (iii) the sets and are relatively compact for all and . The equivalence between (i) and (iii) was recently proven in the case of arbitrary Hilbert spaces by Brown and ülger. It
is also shown that (i) and (ii) are equivalent for subspaces . This result is optimal in the sense that for there is a DPP-subspace that fails to be isomorphic to a subspace of .
Received January 9, 1998; in final form October 1, 1998 相似文献
7.
Elói Medina Galego 《Monatshefte für Mathematik》2002,136(2):87-97
We study the relation of to the subspaces and quotients of Banach spaces of continuous vector-valued functions , where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of totally incomparable to X contains a copy of complemented in . This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of which contain no copy of are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of which is quotient incomparable to X, contains a complemented copy of . Finally we present some more geometric properties of spaces.
Received 8 November 2000; in revised form 7 December 2001 相似文献
8.
J. P. Moreno 《Monatshefte für Mathematik》2007,152(3):255-263
This paper is motivated by recent attempts to investigate classical notions from finite-dimensional convex geometry in spaces
of continuous functions. Let
be the family of all closed, convex and bounded subsets of C(K) endowed with the Hausdorff metric. A completion of
is a diametrically maximal set
satisfying A ⊂ D and diam A = diam D. Using properties of semicontinuous functions and an earlier result by Papini, Phelps and the author [12], we characterize
the family γ(A) of all possible completions of
. We give also a formula which calculates diam γ(A) and prove finally that, if K is a Hausdorff compact space with card K > 1, then the family of those elements of
having a unique completion is uniformly very porous in
with a constant of lower porosity greater than or equal to 1/3. 相似文献
9.
We prove that the composition S(u1, …, un) of a multilinear multiple 2-summing operator S with 2-summing linear operators uj is nuclear, generalizing a linear result of Grothendieck.
Both authors were partially supported by DGICYT grant BMF2001-1284. 相似文献
10.
Michael Kunzinger 《Monatshefte für Mathematik》2002,137(1):31-49
Based on Colombeau’s theory of algebras of generalized functions we introduce the concepts of generalized functions taking
values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic properties,
in particular with respect to some new point value concepts for generalized functions and indicate applications of the resulting
theory in general relativity.
Received February 13, 2002 相似文献
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Vyacheslav V. Chistyakov 《Monatshefte für Mathematik》2002,137(2):99-114
We show that the Hardy space of functions of two variables with finite total variation is a Banach algebra under the pointwise
operations and a suitably chosen norm. Then we characterize Nemytskii superposition operators, which map the Hardy space into
itself and satisfy the global Lipschitz condition.
Received 7 June 2001; in revised form 8 January 2002 相似文献
13.
Aleksej Turnšek 《Monatshefte für Mathematik》2001,132(4):349-354
Let denote the von Neumann–Schatten class, its norm and let be an elementary operator defined by . We shall characterize those operators which are orthogonal to the range of in the sense that for all . The main results of this paper are: If and (i) if A, C, respectively B, D are commuting normal operators with , or (ii) if A, B are contractions and , then is orthogonal to the range of if and only of S is in the kernel of . Furthermore, in both cases, the algebraic direct sum satisfies .
(Received 9 February 2000; in revised form 21 February, 2001) 相似文献
14.
In [7], Nogueira and Rudolph proved that for irreducible permutations not of rotation class almost every (a.e.) interval
exchange transformation (i.e.t.) is topological weak mixing. It is conjectured that the claim holds if topological weak mixing
is replaced by weak mixing. Here we study the behaviour of eigenfunctions of i.e.t. Our analysis gives alternative proofs
of results due to Katok and Stepin [4] and Veech [10]: for certain permutations a.e. i.e.t. is weak mixing and for irreducible
permutations a.e. i.e.t. is totally ergodic.
(Received 1 February 2001) 相似文献
15.
We prove that in a Banach space admitting a separating polynomial, each weakly null normalized sequence has a subsequence
which is equivalent to the usual basis of some , p an even integer. We show that for each even integer p, the Schatten class admits a separating polynomial. For a space with a basis admitting a 4-homogeneous separating polynomial, we relate the unconditionality
of the basis with the existence of certain type of polynomials defined in terms of infinite symmetric matrices. We find relations
between the properties of the entries of these matrices and the geometrical structure of the space. Finally we study the existence
of convex 4-homogeneous separating polynomials.
Received 3 January 2001 相似文献
16.
In the first paper of this series (Daniel Alpay, Tomas Azizov, Aad Dijksma, and Heinz Langer: The Schur algorithm for generalized
Schur functions I: coisometric realizations, Operator Theory: Advances and Applications 129 (2001), pp. 1–36) it was shown
that for a generalized Schur function s(z), which is the characteristic function of a coisometric colligation V with state space being a Pontryagin space, the Schur transformation corresponds to a finite-dimensional reduction of the
state space, and a finite-dimensional perturbation and compression of its main operator. In the present paper we show that
these formulas can be explained using simple relations between V and the colligation of the reciprocal s(z)−1 of the characteristic function s(z) and general factorization results for characteristic functions.
Received October 31, 2001; in revised form August 21, 2002
RID="a"
ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday 相似文献
17.
In a recent paper, Ghenciu and Lewis studied strong Dunford-Pettis sets and made the following two assertions:
While the statements are correct, the proofs are flawed. The difficulty with the proofs is discussed, and a fundamental result
of Elton is used to establish a simple lemma which leads to quick proofs of both (1) and (2).
The online version of the original article can be found at . 相似文献
(1) | The Banach space X * contains a nonrelatively compact strong Dunford-Pettis set if and only if ℓ∞ ↪ X *. |
(2) | If c 0 ↪ Y and H is a complemented subspace of X so that H * is a strong Dunford-Pettis space, then W(X, Y) is not complemented in L(X, Y). |
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We study differences of weighted composition operators between weighted Banach spaces H
ν
∞ of analytic functions with weighted sup-norms and give an expression for the essential norm of these differences. We apply
our result to estimate the essential norm of differences of composition operators acting on Bloch-type spaces.
Authors’ addresses: Mikael Lindstr?m, Department of Mathematics, Abo Akademi University, FIN 20500 Abo, Finland; Elke Wolf,
Mathematical Institute, University of Paderborn, D-33095 Paderborn, Germany 相似文献