Search results for "Tensor"
showing 10 items of 550 documents
Automatic continuity of generalized local linear operators
1980
In this note, we present a general automatic continuity theory for linear mappings between certain topological vector spaces. The theory applies, in particular, to local operators between spaces of functions and distributions, to algebraic homomorphisms between certain topological algebras, and to linear mappings intertwining generalized scalar operators.
Weakly uniformly continuous holomorphic functions and the approximation property
2001
Abstract We study the approximation property for spaces of Frechet and Gâteaux holomorphic functions which are weakly uniformly continuous on bounded sets. We show when U is a balanced open subset of a Baire or barrelled metrizable locally convex space, E , that the space of holomorphic functions which are weakly uniformly continuous on U -bounded sets has the approximation property if and only if the strong dual of E , E ′ b , has the approximation property. We also characterise the approximation property for these spaces of vector-valued holomorphic functions in terms of the tensor product of the corresponding space of scalar-valued holomorphic functions and the range space.
On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials
2007
Given an operator ideal I, we study the multi-ideal I ο L and the polynomial ideal I ο P). The connection with the linearizations of these mappings on projective symmetric tensor products is investigated in detail. Applications to the ideals of strictly singular and absolutely summing linear operators are obtained.
Existence of Unconditional Bases in Spaces of Polynomials and Holomorphic Functions
2002
Our main result shows that every Montel Kothe echelon or coechelon space E of order 1 < p ≤ ∞ is nuclear if and only if for every (some) m ≥ 2 the space ((mE), τ0) of m-homegeneus polynomials on E endowed with the compact-open topology τ0 has an unconditional basis if and only if the space (ℋ(E), τδ) of holomorphic functions on E endowed with the bornological topology τδ associated to τ0 has an unconditional basis (for coechelon spaces τδ equals τ0). The main idea is to extend the concept of the Gordon-Lewis property from Banach to Frechet and (DF) spaces. In this way we obtain techniques which are used to characterize the existence of unconditional basis in spaces of m-th (symmetric) tenso…
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…
Convolution of three functions by means of bilinear maps and applications
1999
When dealing with spaces of vector-valued analytic functions there is a natural way to understand multipliers between them. If X and Y are Banach spaces and L(X,Y ) stands for the space of linear and continuous operators we may consider the convolution of L(X,Y )-valued analytic functions, say F (z) = ∑ n=0∞ Tnz , and X-valued polynomials, say f(z) = ∑m n=0 xnz , to get the Y -valued function F ∗ f(z) = ∑ Tn(xn)z. The second author considered such a definition and studied multipliers between H(X) and BMOA(Y ) in [5]. When the functions take values in a Banach algebra A then the natural extension of multiplier is simply that if f(z) = ∑ anz n and g(z) = ∑ bnz , then f ∗ g(z) = ∑ an.bnz n whe…
ON TOPOLOGICAL SPACES WITH A UNIQUE QUASI-PROXIMITY
1994
Abstract Trying to solve the question of whether every T 1 topological space with a unique compatible quasi-proximity should be hereditarily compact, we show that it is true for product spaces as well as for locally hereditarily Lindelof spaces.
Simultaneous bilateral occurrence of a M. extensor digiti medii and a M. extensor digitorum brevis.
1993
Summary For the first time, the simultaneous and bilateral occurrence of two variants of the extensors of the fingers, M. extensor digiti medii and M. extensor digitorum brevis, is reported. The extensor of the middle finger arises from the distal fourth of the radius and runs to the base of the proximal phalanx. The short extensor of the fingers arises from the metacarpal region and inserts into the dorsal aponeurosis. Both muscles are innervated by the R. profundus n. radialis.
Gluon mass generation in the presence of dynamical quarks
2013
We study in detail the impact of dynamical quarks on the gluon mass generation mechanism, in the Landau gauge, for the case of a small number of quark families. As in earlier considerations, we assume that the main bulk of the unquenching corrections to the gluon propagator originates from the fully dressed quark-loop diagram. The nonperturbative evaluation of this diagram provides the key relation that expresses the unquenched gluon propagator as a deviation from its quenched counterpart. This relation is subsequently coupled to the integral equation that controls the momentum evolution of the effective gluon mass, which contains a single adjustable parameter; this constitutes a major impr…
Automatic Segmentation and Enhancement of Pavement Cracks Based on 3D Pavement Images
2019
Pavement cracking is a significant symptom of pavement deterioration and deficiency. Conventional manual inspections of road condition are gradually replaced by novel automated inspection systems. As a result, a great amount of pavement surface information is digitized by these systems with a high resolution. With pavement surface data, pavement cracks can be detected using crack detection algorithms. In this paper, a fully automated algorithm for segmenting and enhancing pavement crack is proposed, which consists of four major procedures. First, a preprocessing procedure is employed to remove spurious noise and rectify the original 3D pavement data. Second, crack saliency maps are segmente…