Abstract
Local spectral theory has been able, under suitable circumstances, to achieve more than its global counterpart. This paper can be regarded as an illustration of this assertion in connection with positive endomorphisms of ordered Banach spaces and Banach lattices, respectively. Naturally, the presence of an ordering cone implies that the majority of the obtained results will concern positive elements of the underlying space.
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References
Colojoară, I.; Foiaş, C.: Theory of generalized spectral operators, Gordon and Breach, New York, 1968.
Főrster, K.H.; Kutzler, K.: Positive Lősungen von Gleichungen mit positive Operatoren, Mathematica ad diem natalem, Festschrift Ernst Mohr zum 75 Geburtstag, TU Berlin, 1985, pp. 53–61.
Meyer—Nieberg, P.: A partial spectral reduction for positive linear operators, Arch. Math. 45(1985), 34–41.
Nelson Jr., P.: Positive solution of positive linear equations, Proc. Amer. Math. Soc. 31(1972), 453–457.
Schaefer, H. H.: Topological vector spaces, Springer, New York—Heidelberg—Berlin, 1974
Schaefer. H.H. : Banach lattices and positive operators, Springer, New York—Heidelberg—Berlin, 1974
Zabreijko, P.P.; Smitskikh, S.V.: A theorem of M.G. Krein and M.A. Rutman, Funct. Anal. Appl. 13(1980), 222–223.
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© 1988 Birkhäuser Verlag Basel
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Főrster, KH., Nagy, B. (1988). On the local Spectral Theory of Positive Operators. In: Arsene, G. (eds) Special Classes of Linear Operators and Other Topics. Operator Theory: Advances and Applications, vol 28. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9164-6_6
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DOI: https://doi.org/10.1007/978-3-0348-9164-6_6
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-1970-0
Online ISBN: 978-3-0348-9164-6
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