Regular operator sampling for parallelograms

2015 ◽  
Author(s):  
Gotz E. Pfander ◽  
David Walnut
Keyword(s):  
Regular Operator

scholarly journals Revisiting Explicit Negation in Answer Set Programming

2019 ◽  
Vol 19 (5-6) ◽  
pp. 908-924
Author(s):  
FELICIDAD AGUADO ◽  
PEDRO CABALAR ◽  
JORGE FANDINNO ◽  
DAVID PEARCE ◽  
GILBERTO PÉREZ ◽  
...  
Keyword(s):  
Answer Set Programming ◽  
Regular Operator ◽  
Strong Negation ◽  
Classical Negation ◽  
Explicit Negation ◽  
Answer Set

AbstractA common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson’s strong negation.

scholarly journals Matrix Regular Operator Spaces

1998 ◽  
Vol 152 (1) ◽  
pp. 136-175 ◽  
Author(s):  
Walter J. Schreiner
Keyword(s):  
Regular Operator ◽  
Operator Spaces

scholarly journals Dunford-Pettis and strongly Dunford-Pettis operators on L1(μ)

1989 ◽  
Vol 31 (1) ◽  
pp. 49-57 ◽  
Author(s):  
James R. Holub
Keyword(s):  
Positive Operator ◽  
Finite Measure ◽  
Regular Operator ◽  
Mathematical Economics ◽  
Canonical Injection ◽  
Do So ◽  
Convergent Sequences

Motivated by a problem in mathematical economics [4] Gretsky and Ostroy have shown [5] that every positive operator T:L1[0, 1] → c0 is a Dunford-Pettis operator (i.e. T maps weakly convergent sequences to norm convergent ones), and hence that the same is true for every regular operator from L1[0, 1] to c0. In a recent paper [6] we showed the converse also holds, thereby characterizing the D–P operators by this condition. In each case the proof depends (as do so many concerning D–P operators on Ll[0, 1]) on the following well-known result (see, e.g., [2]): If μ is a finite measure, an operator T:L1(μ) → E is a D–P operator is compact, where i:L∞(μ) → L1(μ) is the canonical injection of L∞(μ) into L1(μ). If μ is not a finite measure this characterization of D–P operators is no longer available, and hence results based on its use (e.g. [5], [6]) do not always have straightforward extensions to the case of operators on more general L1(μ) spaces.

scholarly journals A note on Dunford-Pettis operators

1987 ◽  
Vol 29 (2) ◽  
pp. 271-273 ◽  
Author(s):  
J. R. Holub
Keyword(s):  
Linear Operator ◽  
Positive Operator ◽  
Continuous Linear Operator ◽  
Positive Operators ◽  
Regular Operator ◽  
Continuous Linear

Talagrand has shown [4, p. 76] that there exists a continuous linear operator from L1[0, 1] to c0 which is not a Dunford-Pettis operator. In contrast to this result, Gretsky and Ostroy [2] have recently proved that every positive operator from L[0, 1] to c0 is a Dunford-Pettis operator, hence that every regular operator between these spaces (i.e. a difference of positive operators) is Dunford-Pettis.

scholarly journals Pseudodifferential operators with non-regular operator-valued symbols

2013 ◽  
Vol 144 (3-4) ◽  
pp. 349-372 ◽  
Author(s):  
Bienvenido Barraza Martínez ◽  
Robert Denk ◽  
Jairo Hernández Monzón
Keyword(s):  
Pseudodifferential Operators ◽  
Regular Operator
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