scholarly journals The Composition Operation on Spaces of Holomorphic Mappings

2020 ◽  
Vol 71 (2) ◽  
pp. 557-572
Author(s):  
María D Acosta ◽  
Pablo Galindo ◽  
Luiza A Moraes
Keyword(s):  
Banach Space ◽  
Complex Banach Space ◽  
Holomorphic Mappings ◽  
Fréchet Space ◽  
Frechet Space ◽  
Linear Subspaces ◽  
Left And Right ◽  
Relationship Of ◽  
The Relationship ◽  
Bounded Sets

Abstract We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.

scholarly journals Semi-normal operators on uniformly smooth Banach spaces

1990 ◽  
Vol 32 (3) ◽  
pp. 273-276 ◽  
Author(s):  
Muneo Chō
Keyword(s):  
Banach Space ◽  
Linear Functional ◽  
Dual Space ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Bounded Linear ◽  
Uniformly Smooth ◽  
Normal Operators ◽  
Uniformly Smooth Banach Spaces ◽  
The Relationship

In this paper we shall examine the relationship between the numerical ranges and the spectra for semi-normal operators on uniformly smooth spaces.Let X be a complex Banach space. We denote by X* the dual space of X and by B(X) the space of all bounded linear operators on X. A linear functional F on B(X) is called state if ∥F∥ = F(I) = 1. When x ε X with ∥x∥ = 1, we denoteD(x) = {f ε X*:∥f∥ = f(x) = l}.

Darboux chart on projective limit of weak symplectic Banach manifold

2015 ◽  
Vol 12 (07) ◽  
pp. 1550072 ◽  
Author(s):  
Pradip Mishra
Keyword(s):  
Banach Space ◽  
Symplectic Structure ◽  
Reflexive Banach Space ◽  
Projective Limit ◽  
Fréchet Space ◽  
Frechet Space ◽  
Banach Manifold ◽  
Boundedness Condition ◽  
Projective System ◽  
Banach Manifolds

Suppose M be the projective limit of weak symplectic Banach manifolds {(Mi, ϕij)}i, j∈ℕ, where Mi are modeled over reflexive Banach space and σ is compatible with the projective system (defined in the article). We associate to each point x ∈ M, a Fréchet space Hx. We prove that if Hx are locally identical, then with certain smoothness and boundedness condition, there exists a Darboux chart for the weak symplectic structure.

scholarly journals Characterizations and properties of graphs of Baire functions

2018 ◽  
Vol 68 (4) ◽  
pp. 789-802
Author(s):  
Balázs Maga
Keyword(s):  
Banach Space ◽  
Topological Space ◽  
Convex Set ◽  
Vertical Section ◽  
Fréchet Space ◽  
Frechet Space ◽  
Similar Question ◽  
Baire Functions

Abstract Let X be a paracompact topological space and Y be a Banach space. In this paper, we will characterize the Baire-1 functions f : X → Y by their graph: namely, we will show that f is a Baire-1 function if and only if its graph gr(f) is the intersection of a sequence $\begin{array}{} \displaystyle (G_n)_{n=1}^{\infty} \end{array}$ of open sets in X × Y such that for all x ∈ X and n ∈ ℕ the vertical section of Gn is a convex set, whose diameter tends to 0 as n → ∞. Afterwards, we will discuss a similar question concerning functions of higher Baire classes and formulate some generalized results in slightly different settings: for example we require the domain to be a metrized Suslin space, while the codomain is a separable Fréchet space. Finally, we will characterize the accumulation set of graphs of Baire-2 functions between certain spaces.

scholarly journals Schwarz-Pick Estimates for Holomorphic Mappings with Values in Homogeneous Ball

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Jianfei Wang
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Arbitrary Order ◽  
Complex Banach Space ◽  
Holomorphic Mappings ◽  
Partial Derivatives ◽  
Carathéodory Metric ◽  
Homogeneous Ball ◽  
Derivatives Of

LetBXbe the unit ball in a complex Banach spaceX. AssumeBXis homogeneous. The generalization of the Schwarz-Pick estimates of partial derivatives of arbitrary order is established for holomorphic mappings from the unit ballBntoBXassociated with the Carathéodory metric, which extend the corresponding Chen and Liu, Dai et al. results.

scholarly journals THE CLOSED RANGE PROPERTY FOR BANACH SPACE OPERATORS

2008 ◽  
Vol 50 (1) ◽  
pp. 17-26 ◽  
Author(s):  
THOMAS L. MILLER ◽  
VLADIMIR MÜLLER
Keyword(s):  
Banach Space ◽  
Complex Plane ◽  
Open Subset ◽  
Weak Topology ◽  
Bounded Operator ◽  
Complex Banach Space ◽  
Fréchet Space ◽  
Closed Range ◽  
Open Set ◽  
Banach Space Operators

AbstractLetTbe a bounded operator on a complex Banach spaceX. LetVbe an open subset of the complex plane. We give a condition sufficient for the mappingf(z)↦ (T−z)f(z) to have closed range in the Fréchet spaceH(V,X) of analyticX-valued functions onV. Moreover, we show that there is a largest open setUfor which the mapf(z)↦ (T−z)f(z) has closed range inH(V,X) for allV⊆U. Finally, we establish analogous results in the setting of the weak–* topology onH(V, X*).

Differentially Talented Females: Some Critical Methodological Issues for the 1980s

1982 ◽  
Vol 50 (2) ◽  
pp. 367-376
Author(s):  
S. Viterbo McCarthy
Keyword(s):  
Information Processing ◽  
Sex Role ◽  
The Other ◽  
Methodological Issues ◽  
Hemispheric Processing ◽  
Personality Correlates ◽  
Left And Right ◽  
Psychometric Studies ◽  
Relationship Of ◽  
The Relationship

Usually psychometric studies have searched for the personality correlates associated with L (high linguistic and low quantitative ability) and Q (low linguistic and high quantitative ability) patterns. Neuropsychological studies, on the other hand, have searched for the cortical processes associated with L and Q patterns or for the psychological functions (presumably linguistic and visuospatial) associated with left- and right-hemispheric processing, respectively. To further our understanding of the relationship of L and Q patterns to personality correlates and modes of information processing and to clarify conflicting interpretations attributed to sex and sex-role factors, a cohort-sequential methodology and a convergence of psychometry with neuropsychology are recommended; three critical methodological issues are explored.

scholarly journals Different laterality indexes are poorly correlated with one another but consistently show the tendency of males and females to be more left- and right-lateralized, respectively

2020 ◽  
Vol 7 (4) ◽  
pp. 191700 ◽  
Author(s):  
Carlos Buenaventura Castillo ◽  
Andy G. Lynch ◽  
Silvia Paracchini
Keyword(s):  
Grip Strength ◽  
Cost Effective ◽  
Strength Analysis ◽  
Dominant Hand ◽  
Sex Effects ◽  
Right Hand ◽  
Left And Right ◽  
Males And Females ◽  
Relationship Of ◽  
The Relationship

The most common way to assess handedness is based on the preferred hand for writing, leading to a binary (left or right) trait. Handedness can also be assessed as a continuous trait with laterality indexes, but these are not time- and cost-effective, and are not routinely collected. Rarely, different handedness measures are collected for the same individuals. Here, we assessed the relationship of preferred hand for writing with four laterality indexes, reported in previous literature, derived from measures of dexterity (pegboard task, marking squares and sorting matches) and strength (grip strength), available in a range of N = 6664–8069 children from the ALSPAC cohort. Although all indexes identified a higher proportion of individuals performing better with their right hand, they showed low correlation with each other (0.08–0.3). Left handers were less consistent compared to right handers in performing better with their dominant hand, but that varied across indexes, i.e. 13% of left handers performed better with their right hand on marking squares compared to 48% for sorting matches and grip strength. Analysis of sex effects on the laterality indexes showed that males and females tend to be, on all measures, more left- and right-lateralized, respectively. Males were also over-represented among the individuals performing equally with both hands suggesting they had a higher tendency to be weakly lateralized. This study shows that different handedness measures tap into different dimensions of laterality and cannot be used interchangeably. The trends observed across indexes for males and females suggest that sex effects should be taken into account in handedness and laterality studies.

scholarly journals Local Uniform Kadec-Klee Property (LUKK) and Modulus of (LUKK)

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Yunan Cui ◽  
Xiaoxia Wang
Keyword(s):  
Banach Space ◽  
Uniform Convexity ◽  
Relationship Of ◽  
The Relationship ◽  
Classical Banach Space

A new geometry property and two new moduli are introduced in Banach space. First, the concept of local uniform Kadec-Klee property (LUKK) is introduced and the implication relationships between LUKK and local near uniform convexity LNUC, uniformly Kadec-Klee (UKK), (H) are investigated in Banach space. Furthermore, the modulus PXLε of (LUKK) and the modulus ΔXLε of LNUC are introduced and the relationship of size between PXLε and ΔXLε is also investigated in Banach space. Finally, several formulas for PXLε are calculated in classical Banach space lp.

scholarly journals Fractional powers of operators defined on a Fréchet space

1984 ◽  
Vol 27 (2) ◽  
pp. 165-180 ◽  
Author(s):  
W. Lamb
Keyword(s):  
Banach Space ◽  
Fractional Power ◽  
Fréchet Space ◽  
Frechet Space ◽  
Fractional Powers ◽  
Fractional Powers Of Operators ◽  
Image Position ◽  
Densely Defined

The problem of finding a suitable representation for a fractional power of an operator defined in a Banach space X has, in recent years, attracted much attention. In particular, Balakrishnan [1], Hovel and Westphal [3] and Komatsu [4] have examined the problem of defining the fractionalpower (–A)α for closed densely-defined operators A such that

A representation theorem for a complete Boolean algebra of projections

1979 ◽  
Vol 83 (3-4) ◽  
pp. 225-237 ◽  
Author(s):  
H. R. Dowson ◽  
T. A. Gillespie
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Boolean Algebra ◽  
Complex Banach Space ◽  
Complex Hilbert Space ◽  
Complete Boolean Algebra ◽  
Norm Topology ◽  
Weak Operator ◽  
Bounded Sets ◽  
Algebra Of Operators

SynopsisLet B be a complete Boolean algebra of projections on a complex Banach space X and let (B) denote the closed algebra of operators generated by B in the norm topology. It is shown that there is a complex Hilbert space H, a complete Boolean algebra B0 of self-adjoint projections on H, and an algebraic isomorphism of B onto B. This isomorphism is bicontinuous when B and B are endowed with the norm topologies, the weak operator topologies or the ultraweak operator topologies. It is also bicontinuous on bounded sets with respect to the strong operator topologies on B and B. As an application, it is shown that the weak and ultraweak operator topologies in fact coincide on B.

Sign in / Sign up

Export Citation Format

Share Document