共查询到20条相似文献,搜索用时 0 毫秒
1.
Denoting byC
wu
p
(E) the algebra of allC
p-real-valued functions on the real Banach spaceE such that the functions and the derivatives are weakly uniformly continuous on bounded subsets, it is known that the algebra homomorphismsA:C
wu
q
(F)C
wu
p
(E) are induced by differentiable mappingsg:EF
**. We prove that, for 1p+1q, the following are equivalent: (a)A is compact; (b)g and its derivatives are compact; (c)gC
wu
p
(E,F
**) (the authors had proved that, forp=q<,A is [weakly] compact if and only ifg is a constant mapping, and it is known that ifq<p, thenA is always induced by a constant mapping and is therefore compact). Also, for an entire function of bounded typegH
b
(U,F), where
is a balanced open subset, andE,F are complex Banach spaces, lettingA:H
b
(F)H
b
(U) be the homomorphism given byA(f)=fg for allfH
b
(F), we prove thatA is compact if and only ifg is compact.Supported in part by DGICYT Grant PB 94-1052 (Spain).Supported in part by DGICYT Grant PB 93-0452 (Spain). 相似文献
2.
Seán Dineen 《Indagationes Mathematicae》2008,19(3):379-389
In this article we show that the pointwise existence of a regulariser for holomorphic Fredhom-valued mappings defined on pseudo-convex domains in Banach spaces with an unconditional basis implies the existence of a holomorphic regulariser. 相似文献
3.
Seán Dineen 《Mathematische Annalen》2006,334(2):395-412
Using tensor products and a generalised spectrum, we extend to infinite dimensional domains classical results on the ideals
generated by a finite or countable set of elements in a Fréchet algebra. 相似文献
4.
We study generated semigroups of those self-mappings of the Hilbert ball which are non-expansive with respect to the hyperbolic
metric. We find optimal convergence rates for such semigroups to interior stationary and boundary sink points. Since the hyperbolic
metric is not defined on the boundary, the usual approach treats these two cases separately. In contrast with this practice,
we use a special non-Euclidean “distance” (which induces the original topology) to present a unified theory. Our approach
leads to new results even in the one-dimensional case. When the semigroups consist of holomorphic self-mappings, we obtain
the rather unexpected phenomenon of universal rates of convergence of an exponential type. In particular, in the case of a
boundary sink point we establish a continuous analog of the celebrated Julia–Wolff–Carathéodory theorem.
Received: January 3, 2001; in final form: November 28, 2001?Published online: October 30, 2002 相似文献
5.
Ariosvaldo M. Jatobá 《Indagationes Mathematicae》2009,20(3):415-426
In this paper we study the relationships between the spaces of entire mappings of bounded type, entire mappings of nuclear bounded type, entire mappings of Pietsch integral bounded type, and entire mappings of Grothendieck integral bounded type. Several results due to Alencar (Proc. Roy. Irish Acad.85A (1985) 131-138) and Cilia and Gutiérrez (J. Aust. Math. Soc.76 (2004) 269-280) for homogeneous polynomials are extended to entire mappings. In the main result we prove that an entire mapping is of nuclear bounded type if and only if it factors through an entire mapping of Pietsch integral bounded type. 相似文献
6.
It is shown that a nuclear Fréchet spaceE has the property (DN) if and only if every holomorphic function onE
*, the strongly dual space ofE, with values in the strongly dual space of a Fréchet spaceF having the property (
) can be represented in the exponential form. Moreover, it is shown that the space of holomorphic functions onC
, the space of all complex number sequences, has a linearly absolutely exponential representation system. But the space of holomorphic functions onE
* does not have such a system whenE is a nuclear Fréchet space that does not have the property (DN).Supported by the State Program for Fundamental Researches in Natural Sciences 相似文献
7.
Daniel Carando Silvia Lassalle Ignacio Zalduendo 《Integral Equations and Operator Theory》2006,54(4):597-602
We give a simple proof of the fact that orthogonally additive polynomials on C(K) are represented by regular Borel measures over K. We also prove that the Aron-Berner extension preserves this class of polynomials. 相似文献
8.
In this paper we establish several new results on the existence and uniqueness of a fixed point for holomorphic mappings and one-parameter semigroups in Banach spaces. We also present an application to operator theory on spaces with an indefinite metric. 相似文献
9.
Jari Taskinen 《Israel Journal of Mathematics》1995,92(1-3):207-219
We prove a universal mapping theorem for “integral” holomorphic mappings on the open unit ball ofC(K). In our theorem, the universal space isC(K), and the universal mapping is increasing in the positive cone ofC(K). 相似文献
10.
We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces, and we define two classes of monotone mappings between an ordered linear space and a metric space (resp. ordered linear space): K-monotone dominated and cone-to-cone monotone mappings. K-monotone dominated mappings naturally generalize mappings with finite variation (in the classical sense) and K-monotone functions defined by Borwein, Burke and Lewis to mappings with domains and ranges of higher dimensions. First, using results of Veselý and Zají?ek, we show some relationships between these classes. Then, we show that every K-monotone function f:X→R, where X is any Banach space, is continuous outside of a set which can be covered by countably many Lipschitz hypersurfaces. This sharpens a result due to Borwein and Wang. As a consequence, we obtain a similar result for K-monotone dominated and cone-to-cone monotone mappings. Finally, we prove several results concerning almost everywhere differentiability (also in metric and w∗-senses) of these mappings. 相似文献
11.
Abstract. Let be open,X a Banach space and . We show that every is holomorphic if and only if every set inX is bounded. Things are different if we assume f to be locally bounded. Then we show that it suffices that is holomorphic for all , where W is a separating subspace of to deduce that f is holomorphic. Boundary Tauberian convergence and membership theorems are proved. Namely, if boundary values (in a weak
sense) of a sequence of holomorphic functions converge/belong to a closed subspace on a subset of the boundary having positive
Lebesgue measure, then the same is true for the interior points of , uniformly on compact subsets. Some extra global majorants are requested. These results depend on a distance Jensen inequality.
Several examples are provided (bounded and compact operators; Toeplitz and Hankel operators; Fourier multipliers and small
multipliers).
Received January 29, 1998; in final form March 8, 1999 / Published online May 8, 2000 相似文献
12.
13.
It is shown that for every quasi-normed ideal ${\cal Q}$ of
n-homogeneous continuous polynomials between
Banach spaces there is a quasi-normed ideal ${\cal A}$ of
n-linear continuous mappings ${\cal A}$ such that
$q \in {\cal Q}$ if and only if the associated n-linear
mapping $\check{q}$ of q is in ${\cal A}$.
Received: 12 March 2001 相似文献
14.
We introduce a general definition of almost
p-summing mappings and
give several concrete examples of such mappings. Some known results are
considerably generalized and we present various situations in which the
space of almost p-summing multilinear
mappings coincides with the whole space of continuous multilinear mappings.
Received: 17 June 2002 相似文献
15.
Warren B. Moors 《Set-Valued Analysis》1995,3(2):129-141
In this paper we characterise, in terms of the upper Dini derivative, the Clarke subdifferential mapping being a minimal weak* cusco, and we show that on any Banach space the Clarke subdifferential mapping of a pseudo-regular or semi-smooth locally Lipschitz function is always a minimal weak* cusco. 相似文献
16.
17.
Hiroshi Sugita 《Probability Theory and Related Fields》1994,100(1):117-130
Summary We show that each holomorphic Wiener function has a skeleton which is intrinsic from several viewpoints. In particular, we study the topological aspects of the skeletons by using the local Taylor expansion for holomorphic Wiener functions.Supported in part by the Grant-in-Aid for Science Research 03740120 Min. Education 相似文献
18.
In this paper we extend and generalize several known estimates for homogeneous polynomials and multilinear mappings on Banach spaces. Applying the theory of absolutely summing nonlinear mappings, we prove that estimates which are known for mappings on ?p spaces in fact hold true for mappings on arbitrary Banach spaces. 相似文献
19.
It is well known that continuous bilinear forms on C(K) × C(K) are 2-dominated. This paper shows that generalizations of this result are not to be expected. The main result asserts that for every
-space E(1 p ), every n 2, every r > 0 and every Banach space F , there exists an n-homogeneous polynomial P : E F such that P is not of type [r], hence P is neither r-dominated nor r-semi-integral (if n = 2 and p = , F is supposed to contain an isomorphic copy of some
, 1q < ).Received: 24 November 2003 相似文献
20.
If points in nontrivial Gleason parts of a uniform Banach algebra have unique representing measures, then the weak and the
norm topology coincide on the spectrum. We derive from this several consequences about weakly compact homomorphisms and discuss
the case of other uniform Banach algebras arising in complex infinite dimensional analysis.
(Received 9 March 1998; in revised form 29 June 1998) 相似文献