Search results for " function"
showing 10 items of 9395 documents
On operator valued sequences of multipliers and R-boundedness
2007
AbstractIn recent papers (cf. [J.L. Arregui, O. Blasco, (p,q)-Summing sequences, J. Math. Anal. Appl. 274 (2002) 812–827; J.L. Arregui, O. Blasco, (p,q)-Summing sequences of operators, Quaest. Math. 26 (2003) 441–452; S. Aywa, J.H. Fourie, On summing multipliers and applications, J. Math. Anal. Appl. 253 (2001) 166–186; J.H. Fourie, I. Röntgen, Banach space sequences and projective tensor products, J. Math. Anal. Appl. 277 (2) (2003) 629–644]) the concept of (p,q)-summing multiplier was considered in both general and special context. It has been shown that some geometric properties of Banach spaces and some classical theorems can be described using spaces of (p,q)-summing multipliers. The p…
Isometries of weighted spaces of holomorphic functions on unbounded domains
2009
We study isometries between weighted spaces of holomorphic functions on unbounded domains in ℂn. We show that weighted spaces of holomorphic functions on unbounded domains may exhibit behaviour different from that observed on bounded domains. We calculate the isometries for specific weights on the complex plane and the right half-plane.
Characterizing varieties of colength ≤4
2009
Let A be an associative algebra over a field F of characteristic zero, and let χ n (A), n = 1,2,…, be the sequence of cocharacters of A. For every n ≥ 1, let l n (A) denote the nth colength of A, counting the number of S n -irreducibles appearing in χ n (A). In this article, we classify the algebras A such that the sequence of colengths l n (A), n = 1,2,…, is bounded by four. Moreover we construct a finite number of algebras A 1,…, A d , such that l n (A) ≤ 4 if and only if A 1,…, A d ∉ var(A).
Internal inverse limits and retractions
2015
We establish equivalences between compacta that admit a sequence of retractions that converge uniformly to the identity map and compacta that are inverse limits on subcompacta with retractions for bonding maps. We give partial answers to questions of Charatonik and Prajs, and of Krasinkiewicz. Our results are related to and use results from another paper of the authors \cite{mp}.
Varieties of superalgebras of almost polynomial growth
2011
Abstract Let V gr be a variety of superalgebras and let c n gr ( V gr ) , n = 1 , 2 , … , be its sequence of graded codimensions. Such a sequence is polynomially bounded if and only if V gr does not contain a list of five superalgebras consisting of a commutative superalgebra, the infinite dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with trivial and natural Z 2 -gradings. In this paper we completely classify all subvarieties of the varieties generated by these five superalgebras, by giving a complete list of finite dimensional generating superalgebras.
Polynomial identities on superalgebras and exponential growth
2003
Abstract Let A be a finitely generated superalgebra over a field F of characteristic 0. To the graded polynomial identities of A one associates a numerical sequence {cnsup(A)}n⩾1 called the sequence of graded codimensions of A. In case A satisfies an ordinary polynomial identity, such sequence is exponentially bounded and we capture its exponential growth by proving that for any such algebra lim n→∞ c n sup (A) n exists and is a non-negative integer; we denote such integer by supexp(A) and we give an effective way for computing it. As an application, we construct eight superalgebras Ai, i=1,…,8, characterizing the identities of any finitely generated superalgebra A with supexp(A)>2 in the f…
Proper identities, Lie identities and exponential codimension growth
2008
Abstract The exponent exp ( A ) of a PI-algebra A in characteristic zero is an integer and measures the exponential rate of growth of the sequence of codimensions of A [A. Giambruno, M. Zaicev, On codimension growth of finitely generated associative algebras, Adv. Math. 140 (1998) 145–155; A. Giambruno, M. Zaicev, Exponential codimension growth of P.I. algebras: An exact estimate, Adv. Math. 142 (1999) 221–243]. In this paper we study the exponential rate of growth of the sequences of proper codimensions and Lie codimensions of an associative PI-algebra. We prove that the corresponding proper exponent exists for all PI-algebras, except for some algebras of exponent two strictly related to t…
Absolutely summing operators on C[0,1] as a tree space and the bounded approximation property
2010
Abstract Let X be a Banach space. For describing the space P ( C [ 0 , 1 ] , X ) of absolutely summing operators from C [ 0 , 1 ] to X in terms of the space X itself, we construct a tree space l 1 tree ( X ) on X. It consists of special trees in X which we call two-trunk trees. We prove that P ( C [ 0 , 1 ] , X ) is isometrically isomorphic to l 1 tree ( X ) . As an application, we characterize the bounded approximation property (BAP) and the weak BAP in terms of X ∗ -valued sequence spaces.
On n–Fold Blocking Sets
1986
An n-fold blocking set is a set of n-disjoint blocking sets. We shall prove upper and lower bounds for the number of components in an n-fold blocking set in projective and affine spaces.
Probabilistic entailment and iterated conditionals
2020
In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval $[0,1]$. We examine the iterated conditional $(B|K)|(A|H)$, by showing that $A|H$ p-entails $B|K$ if and only if $(B|K)|(A|H) = 1$. Then, we show that a p-consistent family $\mathcal{F}=\{E_1|H_1,E_2|H_2\}$ p-entails a conditional event $E_3|H_3$ if and only if $E_3|H_3=1$, or $(E_3|H_3)|QC(\mathcal{S})=1$ for some nonempty subset $\mathcal{S}$ of $\mathcal{F}$, where $QC(\mathcal{S})$ is the quasi conjunction of the conditional events in $\mathcal{S}$. Then, we examine the inference rules $A…