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1.
Shaoqiang Shang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(6):3009-3020
Criteria for weak uniform rotundity and reflexivity of Musielak-Orlicz function spaces of Bochner type equipped with the Luxemburg norm are given. Although, criteria for uniform Gateaux differentiability and weak uniform rotundity of Musielak-Orlicz function spaces of real functions equipped with the Luxemburg norm were known, they can be also easily deduced from our main results. 相似文献
2.
It is shown that all Banach space operators which have Fourier
type p(1 < p 2) with respect to a second countable
locally compact abelian group G also have
Fourier type p with
respect to every closed discrete subgroup H
of G. The same
statement holds for any closed subgroup H
of G when p = 2.
Also shown as a corollary is that Fourier type 2 operators have
Walsh type 2.
Received: 10 June 2002 相似文献
3.
Let A and B be C*-algebras. A linear map T : A → B is said to be a *-homomorphism at an element z ∈ A if ab* = z in A implies T (ab*) = T (a)T (b)* = T (z), and c*d = z in A gives T (c*d) = T (c)*T (d) = T (z). Assuming that A is unital, we prove that every linear map T : A → B which is a *-homomorphism at the unit of A is a Jordan *-homomorphism. If A is simple and infinite, then we establish that a linear map T : A → B is a *-homomorphism if and only if T is a *-homomorphism at the unit of A. For a general unital C*-algebra A and a linear map T : A → B, we prove that T is a *-homomorphism if, and only if, T is a *-homomorphism at 0 and at 1. Actually if p is a non-zero projection in A, and T is a ?-homomorphism at p and at 1 ? p, then we prove that T is a Jordan *-homomorphism. We also study bounded linear maps that are *-homomorphisms at a unitary element in A. 相似文献
4.
Henryk Hudzik 《Indagationes Mathematicae》2006,17(3):373-395
General results saying that a point x of the unit sphere S(E) of a Köthe space E is an extreme point (a strongly extreme point) [an SU-point] of B(E) if and only if ‖x‖ is an extreme point (a strongly extreme point) [an SU-point] of B(E+) and ‖x‖ is a UM-point (a ULUM-point) [nothing more] of E are proved. These results are applied to get criteria for extreme points and SU-points of the unit ball in Caldern-Lozanovski spaces which refer to problem XII from [5]. Strongly extreme points in these spaces are also discussed. 相似文献
5.
We construct a family (Xγ) of reflexive Banach spaces with long (countable as well as uncountable) transfinite bases but with no unconditional basic sequences. The method we introduce to achieve this allows us to considerably control the structure of subspaces of the resulting spaces as well as to precisely describe the corresponding spaces on non-strictly singular operators. For example, for every pair of countable ordinals γ,β, we are able to decompose every bounded linear operator from Xγ to Xβ as the sum of a diagonal operator and an strictly singular operator. We also show that every finite-dimensional subspace of any member Xγ of our class can be moved by and (4+?)-isomorphism to essentially any region of any other member Xδ or our class. Finally, we find subspaces X of Xγ such that the operator space L(X,Xγ) is quite rich but any bounded operator T from X into X is a strictly singular pertubation of a scalar multiple of the identity. 相似文献
6.
Paweł Foralewski Henryk Hudzik Lucjan Szymaszkiewicz 《Nonlinear Analysis: Theory, Methods & Applications》2008
We give some criteria for extreme points and strong U-points in generalized Orlicz–Lorentz sequence spaces, which were introduced in [P. Foralewski, H. Hudzik, L. Szymaszkiewicz, On some geometric and topological properties of generalized Orlicz–Lorentz sequence spaces, Math. Nachr. (in press)] (cf. [G.G. Lorentz, An inequality for rearrangements, Amer. Math. Monthly 60 (1953) 176–179; M. Nawrocki, The Mackey topology of some F-spaces, Ph.D. Dissertation, Adam Mickiewicz University, Poznań, 1984 (in Polish)]). Some examples show that in these spaces the notion of the strong U-point is essentially stronger than the notion of the extreme point. This paper is related to the results from [A. Kamińska, Extreme points in Orlicz–Lorentz spaces, Arch. Math. 55 (1990) 173–180] (see Remark 1). 相似文献
7.
A Banach space is hereditarily finitely decomposable if it does not
contain finite direct sums of infinite dimensional subspaces with
arbitrarily large number of summands. Here we show that the class of all
hereditarily finitely decomposable Banach spaces has the three-space
property. Moreover we show that the corresponding class defined in terms
of quotients has also the three-space property. 相似文献
8.
F. García 《Archiv der Mathematik》2005,85(3):240-247
In this work we prove a result that provides us an equivalent LUR norm in a normed space whenever it has the property of denting and compact faces in the unit ball; we obtain this result after applying the main result of [11]. In the last part of the paper we obtain our main result that gives us a universal map between dentability and quasi-dentability indices.Received: 29 July 2004; revised: 31 January 2005 相似文献
9.
In this article, we prove the following results: (1) A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; (2) A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set. 相似文献
10.
Casey Kelleher 《Topology and its Applications》2012,159(3):749-755
Enflo (1969) [4] constructed a countable metric space that may not be uniformly embedded into any metric space of positive generalized roundness. Dranishnikov, Gong, Lafforgue and Yu (2002) [3] modified Enflo?s example to construct a locally finite metric space that may not be coarsely embedded into any Hilbert space. In this paper we meld these two examples into one simpler construction. The outcome is a locally finite metric space (Z,ζ) which is strongly non-embeddable in the sense that it may not be embedded uniformly or coarsely into any metric space of non-zero generalized roundness. Moreover, we show that both types of embedding may be obstructed by a common recursive principle. It follows from our construction that any metric space which is Lipschitz universal for all locally finite metric spaces may not be embedded uniformly or coarsely into any metric space of non-zero generalized roundness. Our construction is then adapted to show that the group Zω=ℵ0⊕Z admits a Cayley graph which may not be coarsely embedded into any metric space of non-zero generalized roundness. Finally, for each p?0 and each locally finite metric space (Z,d), we prove the existence of a Lipschitz injection f:Z→?p. 相似文献
11.
Valentin Ferenczi 《Advances in Mathematics》2007,213(1):462-488
There exists a real hereditarily indecomposable Banach space X=X(C) (respectively X=X(H)) such that the algebra L(X)/S(X) is isomorphic to C (respectively to the quaternionic division algebra H).Up to isomorphism, X(C) has exactly two complex structures, which are conjugate, totally incomparable, and both hereditarily indecomposable. So there exist two Banach spaces which are isometric as real spaces but totally incomparable as complex spaces. This extends results of J. Bourgain and S. Szarek [J. Bourgain, Real isomorphic complex Banach spaces need not be complex isomorphic, Proc. Amer. Math. Soc. 96 (2) (1986) 221-226; S. Szarek, On the existence and uniqueness of complex structure and spaces with “few” operators, Trans. Amer. Math. Soc. 293 (1) (1986) 339-353; S. Szarek, A superreflexive Banach space which does not admit complex structure, Proc. Amer. Math. Soc. 97 (3) (1986) 437-444], and proves that a theorem of G. Godefroy and N.J. Kalton [G. Godefroy, N.J. Kalton, Lipschitz-free Banach spaces, Studia Math. 159 (1) (2003) 121-141] about isometric embeddings of separable real Banach spaces does not extend to the complex case.The quaternionic example X(H), on the other hand, has unique complex structure up to isomorphism; other examples with a unique complex structure are produced, including a space with an unconditional basis and non-isomorphic to l2. This answers a question of S. Szarek in [S. Szarek, A superreflexive Banach space which does not admit complex structure, Proc. Amer. Math. Soc. 97 (3) (1986) 437-444]. 相似文献
12.
Elói Medina Galego 《Archiv der Mathematik》2005,85(5):433-439
Let X and Y be Banach spaces such that each of them is isomorphic to a complemented subspace of the other. In 1996, W. T. Gowers solved
the Schroeder-Bernstein Problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we give suitable conditions on finite sums of X and Y to yield that Xm is isomorphic to Yn for some
In other words, we obtain some extensions of the well-known Pełczyński decomposition method in Banach spaces. In order to
do this, we introduce the notion of Nearly Schroeder-Bernstein Quadruples for Banach spaces and pose a Conjecture to characterise
them.
Received: 5 January 2005 相似文献
13.
Petr Hájek 《Journal of Functional Analysis》2004,211(1):163-172
A new rotundity property of Day's norm on c0(Γ) is introduced. This property provides in particular a renorming characterization of the class of all reflexive Banach spaces. 相似文献
14.
Elói Medina Galego 《Results in Mathematics》2007,50(1-2):27-41
Suppose that X and Y are Banach spaces complemented in each other with supplemented subspaces A and B. In 1996, W. T. Gowers solved the Schroeder–Bernstein problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain some suitable conditions involving the spaces A and B to yield that X is isomorphic to Y or to provide that at least X
m is isomorphic to Yn
for some m, n ∈ IN*. So we get some decomposition methods in Banach spaces via supplemented subspaces resembling Pełczyński’s decomposition methods.
In order to do this, we introduce several notions of Schroeder–Bernstein Quadruples acting on the spaces X, Y, A and B. Thus, we characterize them by using some Banach spaces recently constructed.
Received: October 4, 2005. 相似文献
15.
The concepts of complex locally uniform rotundity and complex locally uniformly rotund point are introduced. The sufficient and necessary conditions of them are given in complex MusielakOrlicz spaces. 相似文献
16.
Ioannis K. Argyros 《Aequationes Mathematicae》1988,36(1):99-111
We apply the method of continuation to study the structure of the solutions of quadratic integral equations for a certain class of kernel functions. 相似文献
17.
F. García 《Topology and its Applications》2006,153(15):2886-2892
In this paper we characterize the class of uniform Eberlein compact spaces through a network condition and also in terms of covering properties for the square of the space. 相似文献
18.
19.
In this paper, a Rogalski–Cornet-type surjectivity theorem without any continuity assumptions is proved. Some stability results for certain set-valued maps based on this result are also discussed. By applying these results to a generalized Leontief input–output inclusion problem, some solvability and stability criteria are obtained. 相似文献
20.
Félix Cabello Sánchez Jesús M.F. Castillo Jesús Suárez 《Nonlinear Analysis: Theory, Methods & Applications》2012
We show that c0 is the only Banach space with unconditional basis that satisfies the equation Ext(X,X)=0. This partially improves an old result by Kalton and Peck. We prove that the Kalton–Peck maps are strictly singular on a number of sequence spaces, including ?p for 0<p<∞, Tsirelson and Schlumprecht spaces and their duals, as well as certain super-reflexive variations of these spaces. In the last section, we give estimates of the projection constants of certain finite-dimensional twisted sums of Kalton–Peck type. 相似文献