scholarly journals Banach lattice sums with hereditary Fatou properties

2014 ◽  
Vol 50 (2) ◽  
pp. 271-282
Author(s):  
Mieczysław Mastyło ◽  
Enrique A. Sánchez-Pérez
Keyword(s):  
Banach Lattice ◽  
Lattice Sums

scholarly journals On the calculation of lattice sums

Physica ◽  
1957 ◽  
Vol 23 (1-5) ◽  
pp. 309-321 ◽  
Author(s):  
B.R.A. Nijboer ◽  
F.W. De Wette
Keyword(s):  
Lattice Sums

Green's tensors and lattice sums for electrostatics and elastodynamics

1997 ◽  
Vol 453 (1958) ◽  
pp. 643-662 ◽  
Author(s):  
A. B. Movchan ◽  
N. A. Nicorovici ◽  
R. C. McPhedran
Keyword(s):  
Lattice Sums

Some simple theorems concerning crystal lattice sums of electric potential, electric field, and electric field gradient in crystals

1967 ◽  
Vol 20 (12) ◽  
pp. 2551 ◽  
Author(s):  
CK Coogan
Keyword(s):  
Electric Field ◽  
Field Gradient ◽  
Electric Potential ◽  
Higher Symmetry ◽  
Lattice Sums ◽  
Symmetry Properties ◽  
Lattice Sum ◽  
Direct Lattice ◽  
Electric Potential Field ◽  
Conver Gence

The conditions under which direct lattice sums of electric potential, field, and field gradient converge are discussed. The analogous conditions under which differences in these lattice sums, for two points in the crystal, converge are also outlined. These conditions are applied to direct lattice sum calculations in crystals in which the ideal lattice is distorted close to a defect of some kind. The conver- gence conditions are then applied to the case of determining the direct lattice sums in crystals in which higher symmetry properties can be invoked, which leads to a knowledge by inspection of the lattice sum at one point in the unit cell.

Tauberian theorems in a Banach lattice, with applications to the LP spaces

1954 ◽  
Vol 50 (2) ◽  
pp. 242-249
Author(s):  
D. C. J. Burgess
Keyword(s):  
Banach Space ◽  
Banach Lattice ◽  
Laplace Transforms ◽  
Tauberian Theorems ◽  
General Argument ◽  
Arbitrary Banach Space ◽  
Lp Spaces ◽  
Special Case

In a previous paper (2) of the author, there was given a treatment of Tauberian theorems for Laplace transforms with values in an arbitrary Banach space. Now, in § 2 of the present paper, this kind of technique is applied to the more special case of Laplace transforms with values in a Banach lattice, and investigations are made on what additional results can be obtained by taking into account the existence of an ordering relation in the space. The general argument is again based on Widder (5) to which frequent references are made.

Linear Dependence of Lattice Sums

1958 ◽  
Vol 110 (1-6) ◽  
pp. 112-126 ◽  
Author(s):  
Pinhas Naor
Keyword(s):  
Linear Dependence ◽  
Lattice Sums

Lattice sums arising from the Poisson equation

2013 ◽  
Vol 46 (11) ◽  
pp. 115201 ◽  
Author(s):  
D H Bailey ◽  
J M Borwein ◽  
R E Crandall ◽  
I J Zucker
Keyword(s):  
Poisson Equation ◽  
Lattice Sums ◽  
The Poisson Equation

scholarly journals Banach spaces with property (w)

1993 ◽  
Vol 35 (2) ◽  
pp. 207-217 ◽  
Author(s):  
Denny H. Leung
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Banach Lattice ◽  
Banach Lattices ◽  
Weakly Compact ◽  
Type Spaces

A Banach space E is said to have Property (w) if every operator from E into E' is weakly compact. This property was introduced by E. and P. Saab in [9]. They observe that for Banach lattices, Property (w) is equivalent to Property (V*), which in turn is equivalent to the Banach lattice having a weakly sequentially complete dual. Thus the following question was raised in [9].Does every Banach space with Property (w) have a weakly sequentially complete dual, or even Property (V*)?In this paper, we give two examples, both of which answer the question in the negative. Both examples are James type spaces considered in [1]. They both possess properties stronger than Property (w). The first example has the property that every operator from the space into the dual is compact. In the second example, both the space and its dual have Property (w). In the last section we establish some partial results concerning the problem (also raised in [9]) of whether (w) passes from a Banach space E to C(K, E).

On the convergence problem for lattice sums

1990 ◽  
Vol 23 (12) ◽  
pp. 2523-2528 ◽  
Author(s):  
J P Buhler ◽  
R E Crandall
Keyword(s):  
Convergence Problem ◽  
Lattice Sums
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