共查询到20条相似文献,搜索用时 31 毫秒
1.
An elementary proof of the (known) fact that each element of the Banach spaceℓ
w
p
(X) of weakly absolutelyp-summable sequences (if 1≤p<∞) in the Banach spaceX is the norm limit of its sections if and only if each element ofℓ
w
p
(X) is a norm null sequence inX, is given. Little modification to this proof leads to a similar result for a family of Orlicz sequence spaces. Some applications
to spaces of compact operators on Banach sequence spaces are considered. 相似文献
2.
We say that a Banach space X satisfies the “descent spectrum equality” (in short, DSE) whenever, for every bounded linear operator T on X, the descent spectrum of T as an operator coincides with the descent spectrum of T as an element of the algebra of all bounded linear operators on X. We prove that the DSE is fulfilled by ℓ1, all Hilbert spaces, and all Banach spaces which are not isomorphic to any of their proper quotients (so, in particular,
by the hereditarily indecomposable Banach spaces [8]), but not by ℓ
p
, for 1 < p ≤ ∞ with p ≠ 2. Actually, a Banach space is not isomorphic to any of its proper quotients if and only if it is not isomorphic to any
of its proper complemented subspaces and satisfies the DSE. 相似文献
3.
Jan van Neerven 《Positivity》2007,11(3):461-467
We give a new proof of a recent characterization by Diaz and Mayoral of compactness in the Lebesgue-Bochner spaces LXp, where X is a Banach space and 1≤ p<∞, and extend the result to vector-valued Banach function spaces EX, where E is a Banach function space with order continuous norm.
The author is supported by the ‘VIDI subsidie’ 639.032.201 in the ‘Vernieuwingsimpuls’ programme of the Netherlands Organization
for Scientific Research (NWO) and by the Research Training Network HPRN-CT-2002-00281. 相似文献
4.
Let X denote a specific space of the class of X
α,p
Banach sequence spaces which were constructed by Hagler and the first named author as classes of hereditarily ℓp Banach spaces. We show that for p > 1 the Banach space X contains asymptotically isometric copies of ℓp. It is known that any member of the class is a dual space. We show that the predual of X contains isometric copies of ℓp where 1/p + 1/q = 1. For p = 1 it is known that the predual of the Banach space X contains asymptotically isometric copies of c
0. Here we give a direct proof of the known result that X contains asymptotically isometric copies of ℓ1. 相似文献
5.
In this paper we study the spaces ∞p(E, X) of p-lattice summing operators from a Banach space E to a Banach lattice X. The main results characterize those E and X for which Δp(E, X) = IIp(E, X) and we show that ∞(E, X)=Δ2(E, X) for an infinite dimensional Banach lattice X of finite cotype if and only if E is isomorphic to a Hilbert space. 相似文献
6.
The class of stable Banach spaces, inspired by the stability theory in mathematical logic, was introduced by Krivine and Maurey
and provided the proper context for the abstract formulation of Aldous’ result of subspaces ofL
1. In this paper we study the wider class of weakly stable Banach spaces, where the exchangeability of the iterated limits
occurs only for sequences belonging to weakly compact subsets, introduced independently by Garling (in an earlier unpublished
version of his expository paper on stable Banach spaces brought recently to our attention) and by the authors. Taking into
account Rosenthal’s application of the study of pointwise compact sets of Baire-1 functions (Rosenthal compact spaces) in
the study of Banach spaces (for whichl
1 does not embed isomorphically) and of the study of Rosenthal compact sets by Rosenthal and Bourgain-Fremlin-Talagrand, we
prove the following analogue of the Krivine-Maurey theorem for weakly stable spaces:If X is infinite dimensional and weakly stable then either l
p for some p≧1or co embeds isomorphically in X (§1). Garling (in the above reference) proved this result under the additional assumption thatX* is separable. We also construct an example of a Banach spaceX which is weakly stable, without an equivalent stable norm, and such thatl
2 embeds isomorphically in every infinite dimensional subspace ofX (§3). 相似文献
7.
A Banach space X will be called extensible if every operator E → X from a subspace E ⊂ X can be extended to an operator X → X. Denote by dens X. The smallest cardinal of a subset of X whose linear span is dense in X, the space X will be called automorphic when for every subspace E ⊂ X every into isomorphism T: E → X for which dens X/E = dens X/TE can be extended to an automorphism X → X. Lindenstrauss and Rosenthal proved that c
0 is automorphic and conjectured that c
0 and ℓ2 are the only separable automorphic spaces. Moreover, they ask about the extensible or automorphic character of c
0(Γ), for Γ uncountable. That c
0(Γ) is extensible was proved by Johnson and Zippin, and we prove here that it is automorphic and that, moreover, every automorphic
space is extensible while the converse fails. We then study the local structure of extensible spaces, showing in particular
that an infinite dimensional extensible space cannot contain uniformly complemented copies of ℓ
n
p
, 1 ≤ p < ∞, p ≠ 2. We derive that infinite dimensional spaces such as L
p
(μ), p ≠ 2, C(K) spaces not isomorphic to c
0 for K metric compact, subspaces of c
0 which are not isomorphic to c
0, the Gurarij space, Tsirelson spaces or the Argyros-Deliyanni HI space cannot be automorphic.
The work of the first author has been supported in part by project MTM2004-02635 相似文献
8.
It is proved using positive definite functions that a normed spaceX is unifomly homeomorphic to a subset of a Hilbert space, if and only ifX is (linearly) isomorphic to a subspace of aL
0(μ) space (=the space of the measurable functions on a probability space with convergence in probability). As a result we get
thatl
p
(respectivelyL
p
(0, 1)), 2<p<∞, is not uniformly embedded in a bounded subset of itself. This answers negatively the question whether every infinite dimensional
Banach space is uniformly homeomorphic to a bounded subset of itself. Positive definite functions are also used to characterize
geometrical properties of Banach spaces.
Partially supported by the National Science Foundation, Grant MCS-79-03322.
Partially supported by the National Science Foundation, Grant MCS-80-06073. 相似文献
9.
S. Bates W. B. Johnson J. Lindenstrauss D. Preiss G. Schechtman 《Geometric And Functional Analysis》1999,9(6):1092-1127
New concepts related to approximating a Lipschitz function between Banach spaces by affine functions are introduced. Results
which clarify when such approximations are possible are proved and in some cases a complete characterization of the spaces
X, Y for which any Lipschitz function from X to Y can be so approximated is obtained. This is applied to the study of Lipschitz and uniform quotient mappings between Banach
spaces. It is proved, in particular, that any Banach space which is a uniform quotient of L
p
, 1 < p < , is already isomorphic to a linear quotient of L
p
.
Submitted: June 1998, revised: December 1998. 相似文献
10.
Dumitru Popa 《Quaestiones Mathematicae》2018,41(5):683-692
We prove two characterizations of new Cohen summing bilinear operators. The first one is: Let X, Y and Z be Banach spaces, 1 < p < ∞, V : X × Y → Z a bounded linear operator and n ≥ 2 a natural number. Then V is new Cohen p-summing if and only if for all Banach spaces X1,?…?, Xn and all p-summing operators U : X1 × · · · × Xn → X, the operator V ? (U, IY) : X1 × · · · × Xn × Y → Z is -summing. The second result is: Let H be a Hilbert space,, Y, Z Banach spaces and V : H × Y → Z a bounded bilinear operator and 1 < p < ∞. Then V is new Cohen p-summing if and only if for all Banach spaces E and all p-summing operators U : E → H, the operator V ? (U, IY) is (p, p*)-dominated. 相似文献
11.
S. J. Dilworth 《Israel Journal of Mathematics》1985,52(1-2):15-27
Suppose that 1<p≦2, 2≦q<∞. The formal identity operatorI:l
p→l
qfactorizes through any given non-compact operator from ap-smooth Banach space into aq-convex Banach space. It follows that ifX is a 2-convex space andY is an infinite dimensional subspace ofX which is isomorphic to a Hilbert space, thenY contains an isomorphic copy ofl
2 which is complemented inX. 相似文献
12.
We prove that if a metric probability space with a usual concentration property embeds into a finite dimensional Banach space
X, then X has a Euclidean subspace of a proportional dimension. In particular this yields a new characterization of weak cotype 2.
We also find optimal lower estimates on embeddings of metric spaces with concentration properties into , generalizing estimates of Bourgain—Lindenstrauss—Milman, Carl—Pajor and Gluskin.
Submitted: February 2001, Revised: August 2001. 相似文献
13.
The ℒ
p
spaces which were introduced by A. Pełczyński and the first named author are studied. It is proved, e.g., that (i)X is an ℒ
p
space if and only ifX* is and ℒ
q
space (p
−1+q
−1=1). (ii) A complemented subspace of an ℒ
p
space is either an ℒ
p
or an ℒ2 space. (iii) The ℒ
p
spaces have sufficiently many Boolean algebras of projections. These results are applied to show thatX is an ℒ∞ (resp. ℒ1) space if and only ifX admits extensions (resp. liftings) of compact operators havingX as a domain or range space. We also prove a theorem on the “local reflexivity” of an arbitrary Banach space.
This research was partially supported by NSF Grant# 8964. 相似文献
14.
Yves Raynaud 《Israel Journal of Mathematics》1989,65(2):197-213
We show that ifl
p(X),p ≠ 2, is finitely crudely representable in an Orlicz spaceL
ϕ (which does not containc
0) then the Banach spaceX is isomorphic to a subspace ofL
p. The same remains true forp = 2 whenL
ϕ is 2-concave or 2-convex, or ifX has local unconditional structure. We extend a theorem of Guerre and Levy to Orlicz function spaces. 相似文献
15.
Yehoram Gordon 《Israel Journal of Mathematics》1969,7(2):151-163
Given 1≦p<∞ and a real Banach spaceX, we define thep-absolutely summing constantμ
p(X) as inf{Σ
i
=1/m
|x*(x
i)|p
p Σ
i
=1/m
‖x
i‖p
p]1
p}, where the supremum ranges over {x*∈X*; ‖x*‖≤1} and the infimum is taken over all sets {x
1,x
2, …,x
m} ⊂X such that Σ
i
=1/m
‖x
i‖>0. It follows immediately from [2] thatμ
p(X)>0 if and only ifX is finite dimensional. In this paper we find the exact values ofμ
p(X) for various spaces, and obtain some asymptotic estimates ofμ
p(X) for general finite dimensional Banach spaces.
This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof.
A. Dvoretzky and Prof. J. Lindenstrauss. 相似文献
16.
F. Weisz 《Acta Mathematica Hungarica》2007,116(1-2):47-59
The duality between martingale Hardy and BMO spaces is generalized for Banach space valued martingales. It is proved that if X is a UMD Banach space and f ∈ L
p(X) for some 1 < p < ∞ then the Vilenkin-Fourier series of f converges to f almost everywhere in X norm, which is the extension of Carleson’s result.
This paper was written while the author was researching at University of Vienna (NuHAG) supported by Lise Meitner fellowship
No. M733-N04. This research was also supported by the Hungarian Scientific Research Funds (OTKA) No. T043769, T047128, T047132. 相似文献
17.
Tetiana V. Bosenko 《Central European Journal of Mathematics》2010,8(2):346-356
A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies ||G + T|| = ||G|| + ||T||. We study the case when either X or Y is a sum X
1⊕F
X
2 of two Banach spaces X
1 and X
2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X
1 and X
2 there exists a Daugavet center acting from X
1⊕F
X
2, and the class of those F such that for some pair of spaces X
1 and X
2 there is a Daugavet center acting into X
1⊕F
X
2. We also present several examples of such Daugavet centers. 相似文献
18.
A. Szankowski 《Israel Journal of Mathematics》1972,11(3):292-296
We construct a separable reflexive Banach spaceX which is complementably universal for all finite dimensional Banach spaces. By this we mean: for every finite dimensional
Banach spaceE there is isometric embeddingi:E→X such that there exists a projectionP: →
→
onto
with ‖P‖=1. 相似文献
19.
We give sufficient conditions on Banach spaces X and Y so that their projective tensor product X ⊗π
Y, their injective tensor product X ⊗ɛ
Y, or the dual (X ⊗π
Y)* contain complemented copies of ℓp. 相似文献
20.
In this article we study the embeddability of cones in a Banach space X. First we prove that c
0 is embeddable in X if and only if its positive cone c0+{c_0^+} is embeddable in X and we study some properties of Banach spaces containing c
0 in the light of this result. So, unlike with the positive cone of ℓ
1 which is embeddable in any non-reflexive space, c0+{c_0^+} has the same behavior as the whole space c
0. In the second part of this article we give a characterization of Grothendieck spaces X according to the geometry of cones of X*. By these results we give a partial positive answer to a problem of J.H. Qiu concerning the geometry of cones. 相似文献