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W. A. Light 《Mathematische Zeitschrift》1986,191(4):633-643
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Summary The projection constants of hyperplanes in the classical sequence spaces (c
0
) and (l
1
) are determined, together with the projections of minimum norm.
Entrata in Redazione I'll dicembre 1972. 相似文献
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Les
aw Skrzypek 《Journal of Approximation Theory》2003,123(2):214-231
We will construct a minimal and co-minimal projection from Lp([0,1]n) onto Lp([0,1]n1)++Lp([0,1]nk), where n=n1++nk (see Theorem 2.9). This is a generalization of a result of Cheney, Halton and Light from (Approximation Theory in Tensor Product Spaces, Lecture Notes in Mathematics, Springer, Berlin, 1985; Math. Proc. Cambridge Philos. Soc. 97 (1985) 127; Math. Z. 191 (1986) 633) where they proved the minimality in the case n=2. We provide also some further generalizations (see Theorems 2.10 and 2.11 (Orlicz spaces) and Theorem 2.8). Also a discrete case (Theorem 2.2) is considered. Our approach differs from methods used in [8,13,20]. 相似文献
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《Journal of Combinatorial Theory, Series A》1987,44(2):229-240
A decent linear space DLS(k) is a linear space with minimal line size at least three and with maximal line size exactly k. Denote by vk (resp. bk) the minimum number of points (resp. lines) in a DLS(k). We determine the numbers vk and bk for all k and prove that each DLS(k) with bk lines has vk points. Thus the DLS(k)'s with bk lines are the minimal linear spaces. 相似文献
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Jacob Steinberg 《Integral Equations and Operator Theory》2000,38(1):81-119
In this study we define some classes of projections in a Hilbert space and extend results obtained in a former paper, [2]. The theory allows better insight into examples described in [2], and it is demonstrated how a certain family of projections can be expressed by means of familiar operators. 相似文献
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Vania Mascioni 《Israel Journal of Mathematics》1989,67(1):82-94
Given ans-number sequences te {h, x, y, c, d, a, Γ}, we find a characterization of the following property of a Banach spaceX:(P
s). There is a constantC>0 such that, for anyn-dimensional subspaceE ofX, we can find a projectionP fromX ontoE with sup
k
ks
k(P)≦Cn. As an application, we prove thatX has weak type 2 if and only ifX is finite dimensionally norming, thus answering a question of Casazza and Shura. Weak Hilbert spaces are also characterized
in a new way, the main tool in the proof being a characterization of weak cotype 2 by means of projections. The latter is
applied to the study of U.A.P., too. 相似文献
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Vladimir G. Troitsky 《Proceedings of the American Mathematical Society》2004,132(4):1177-1180
We extend the method of minimal vectors to arbitrary Banach spaces. It is proved, by a variant of the method, that certain quasinilpotent operators on arbitrary Banach spaces have hyperinvariant subspaces.
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Parallel to the study of finite-dimensional Banach spaces, there is a growing interest in the corresponding local theory of operator spaces. We define a family of Hilbertian operator spaces , , generalizing the row and column Hilbert spaces and , and we show that an atomic subspace that is the range of a contractive projection on is isometrically completely contractive to an -sum of the and Cartan factors of types 1 to 4. In particular, for finite-dimensional , this answers a question posed by Oikhberg and Rosenthal. Explicit in the proof is a classification up to complete isometry of atomic w-closed -triples without an infinite-dimensional rank 1 w-closed ideal.
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R. S. Ismagilov 《Functional Analysis and Its Applications》1999,33(4):270-279
The minimal width of an arbitrary metric space is defined as the greatest lower bound of its Kolmogorov widths under all isometric embeddings in all possible Banach spaces and is computed or estimated in a number of examples. Supported by RFBR grant No. 96-15-96249. Human Moscow State Technical University. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 33, No. 4, 49, October–December, 1999. Translated by R. S. Ismagilov 相似文献
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The paper is a survey on the action of Bergman type projections on various Lp on three types of holomorphic function spaces: weighted Bergman spaces, the Bloch spaces. The focus is space, and diagonal Besov spaces. 相似文献
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James E. Jamison 《Linear algebra and its applications》2007,420(1):29-33
In this paper we show that the bicircular projections are precisely the Hermitian projections and prove some immediate consequences of this result. 相似文献