# On invariant elements for positive operators.

Revista Matemática de la Universidad Complutense de Madrid (1997)

- Volume: 10, Issue: 1, page 85-106
- ISSN: 1139-1138

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topZaharopol, R.. "On invariant elements for positive operators.." Revista Matemática de la Universidad Complutense de Madrid 10.1 (1997): 85-106. <http://eudml.org/doc/44243>.

@article{Zaharopol1997,

abstract = {In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting; that is why our approach is different. We do not use Banach limits and the invariant elements we come up with are much easier to describe than the ones constructed involving Banach limits.},

author = {Zaharopol, R.},

journal = {Revista Matemática de la Universidad Complutense de Madrid},

keywords = {Espacio topológico compacto; Retículo de Banach; Operadores lineales; Invariantes; existence of nonzero positive invariant elements; positive operator in Riesz spaces; Banach lattices with order continuous norms; KB-spaces; Banach limits},

language = {eng},

number = {1},

pages = {85-106},

title = {On invariant elements for positive operators.},

url = {http://eudml.org/doc/44243},

volume = {10},

year = {1997},

}

TY - JOUR

AU - Zaharopol, R.

TI - On invariant elements for positive operators.

JO - Revista Matemática de la Universidad Complutense de Madrid

PY - 1997

VL - 10

IS - 1

SP - 85

EP - 106

AB - In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting; that is why our approach is different. We do not use Banach limits and the invariant elements we come up with are much easier to describe than the ones constructed involving Banach limits.

LA - eng

KW - Espacio topológico compacto; Retículo de Banach; Operadores lineales; Invariantes; existence of nonzero positive invariant elements; positive operator in Riesz spaces; Banach lattices with order continuous norms; KB-spaces; Banach limits

UR - http://eudml.org/doc/44243

ER -

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