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1.
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
2.
In this article we study the existence of range projections in rings with involution, relating it to the existence of the Moore-Penrose inverse. The results are applied to the solution of the equation xbx = x in rings with involution, extending the results of Greville for matrices. Simpler new proofs are given of the Moore-Penrose invertibility of regular elements in rings with involution, and of the Ljance's formula. 相似文献
3.
Bibasic sequences of Singer are used to show that ℓ1 embeds complementably in the Banach space X if and only if X* contains a non-relatively compact strong Dunford–Pettis set. Spaces of operators and strongly additive vector measures are
also discussed.
An erratum to this article is available at . 相似文献
4.
On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form
We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12]. 相似文献
5.
We analyze relations between various forms of energies (reciprocal capacities), the transfinite diameter, various Chebyshev
constants and the so-called rendezvous or average number. The latter is originally defined for compact connected metric spaces
(X,d) as the (in this case unique) nonnegative real number r with the property that for arbitrary finite point systems {x
1, …, x
n
} ⊂ X, there exists some point x ∈ X with the average of the distances d(x,x
j
) being exactly r. Existence of such a miraculous number has fascinated many people; its normalized version was even named “the magic number”
of the metric space. Exploring related notions of general potential theory, as set up, e.g., in the fundamental works of Fuglede
and Ohtsuka, we present an alternative, potential theoretic approach to rendezvous numbers. 相似文献
6.
B. Kuzma 《Monatshefte für Mathematik》2003,139(4):271-274
It shown that a linear, surjective mapping which preserves paracontractions in both directions (relative to Euclidean norm) is an (anti)isometry. This is no longer the case if it preserves paracontractions in one direction only.This work was supported by grants from the Ministry of Science and Technology of Slovenia.Received February 4, 2002; in revised form September 20, 2002
Published online May 9, 2003 相似文献
7.
Harro Walk 《Monatshefte für Mathematik》2005,144(4):329-346
For Kolmogorovs strong law of large numbers an alternative short proof is given which weakens Etemadis condition of pairwise independence. The argument uses the known – and elementary – equivalence of (Cesàro) C1- and C2-summability for one-sided bounded sequences. Also other strong laws of large numbers are established, in part via Borel summability. 相似文献
8.
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
9.
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
10.
We introduce the classes of locally convex spaces with the local Dunford-Pettis property and locally dual Schur spaces. We
examine their properties and their relationship to other classes of locally convex spaces. In the class of locally convex
spaces with the local Dunford-Pettis property all polynomials are weakly sequentially continuous whereas in the class of locally
dual Schur spaces all polynomials are weakly continuous on bounded sets.
Research supported by Science Foundation Ireland, Basic Research Grant 2004. 相似文献
11.
M. T. Karaev 《Monatshefte für Mathematik》2008,155(2):161-166
In this article we give, in terms of so-called Berezin symbols, some necessary conditions for the solvability of the Riccati
equation
on the set
of all Toeplitz operators on the Hardy space
.
Author’s address: Department of Technical Programs, Isparta (MYO) Vocational School, Suleyman Demirel University, 32260 Isparta,
Turkey 相似文献
12.
Michael Voit 《Monatshefte für Mathematik》2005,145(3):247-260
Let (Bt)t ≥ 0 be a Brownian motion on
with the corresponding Gaussian convolution semigroup (μt)t ≥ 0 and generator L. We show that algebraic relations between L and the generators of the matrix semigroups
lead to
for t → s, k ≥ 1, and all coordinates i,j. These relations will form the basis for a martingale characterization of (Bt)t ≥ 0 in terms of generalized heat polynomials. This characterization generalizes a corresponding result for the Brownian motion on
in terms of Hermite polynomials due to J. Wesolowski and may be regarded as a variant of the Lévy characterization without continuity assumptions. 相似文献
13.
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
14.
Filippo Tolli 《Monatshefte für Mathematik》2001,133(2):163-173
We present a local limit theorem for a measure on the special linear group with entries in a local field.
(Received 20 March 2000; in revised form 8 September 2000) 相似文献
15.
Under a general hypothesis an expanding map T of a Riemannian manifold M is known to preserve a measure equivalent to the Liouville measure on that manifold. As a consequence of this and Birkhoff’s
pointwise ergodic theorem, the orbits of almost all points on the manifold are asymptotically distributed with regard to this
Liouville measure. Let T be Lipschitz of class τ for some τ in (0,1], let Ω(x) denote the forward orbit closure of x and for a positive real number δ and let E(x0, δ) denote the set of points x in M such that the distance from x0 to Ω is at least δ. Let dim A denote the Hausdorff dimension of the set A. In this paper we prove a result which implies that there is a constant C(T) > 0 such that
if τ = 1 and
if τ < 1. This gives a quantitative converse to the above asymptotic distribution phenomenon. The result we prove is of sufficient
generality that a similar result for expanding hyperbolic rational maps of degree not less than two follows as a special case. 相似文献
16.
C. G. Madonna 《Monatshefte für Mathematik》2005,146(4):333-339
We give infinitely many examples in which the moduli space of rank 2 H-stable sheaves on a K3 surface S endowed by a polarization H of degree 2g – 2, with Chern classes c1 = H and c2 = g – 1, is birationally equivalent to the Hilbert scheme S[g – 4] of zero dimensional subschemes of S of length g – 4. We get in this way a partial generalization of results from [5] and [1]. 相似文献
17.
We introduce the class of Orlicz-Pettis polynomials between Banach spaces, defined by their action on weakly unconditionally
Cauchy series. We give a number of equivalent definitions, examples and counterexamples which highlight the differences between
these polynomials and the corresponding linear operators.
(Received 17 May 1999; in revised form 6 October 1999) 相似文献
18.
By estimating the subgroup numbers associated with various classes of large groups, we exhibit a number of new phenomena in the theory of subgroup growth. 相似文献
19.
For 1 ≤ i < j < d, a j-dimensional subspace L of
and a convex body K in
, we consider the projection K|L of K onto L. The directed projection function v
i,j
(K;L,u) is defined to be the i-dimensional size of the part of K|L which is illuminated in direction u ∈ L. This involves the i-th surface area measure of K|L and is motivated by Groemer’s [17] notion of semi-girth of bodies in
. It is well-known that centrally symmetric bodies are determined (up to translation) by their projection functions, we extend
this by showing that an arbitrary body is determined by any one of its directed projection functions. We also obtain a corresponding
stability result. Groemer [17] addressed the case i = 1, j = 2, d = 3. For j > 1, we then consider the average of v
1,j
(K;L,u) over all spaces L containing u and investigate whether the resulting function
determines K. We will find pairs (d,j) for which this is the case and some pairs for which it is false. The latter situation will be seen to be related to some
classical results from number theory. We will also consider more general averages for the case of centrally symmetric bodies.
The research of the first author was supported in part by NSF Grant DMS-9971202 and that of the second author by a grant from
the Volkswagen Foundation. 相似文献
20.
Horst Alzer 《Monatshefte für Mathematik》2000,131(3):179-188
A classical inequality for Euler’s gamma function states that
for all and with . We prove the following extension of this result. Let be the weighted power mean of of order r. The inequality
holds for all and with if and only if
(Received 3 April 2000; in revised form 26 June 2000) 相似文献