Displaying similar documents to “Multiplicative representation of bilinear operators.”

On M-operators of q-lattices

Radomír Halaš (2002)

Discussiones Mathematicae - General Algebra and Applications

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It is well known that every complete lattice can be considered as a complete lattice of closed sets with respect to appropriate closure operator. The theory of q-lattices as a natural generalization of lattices gives rise to a question whether a similar statement is true in the case of q-lattices. In the paper the so-called M-operators are introduced and it is shown that complete q-lattices are q-lattices of closed sets with respect to M-operators.

Regular vector lattices of continuous functions and Korovkin-type theorems-Part II

Francesco Altomare, Mirella Cappelletti Montano (2006)

Studia Mathematica

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By applying the results of the first part of the paper, we establish some Korovkin-type theorems for continuous positive linear operators in the setting of regular vector lattices of continuous functions. Moreover, we present simple methods to construct Korovkin subspaces for finitely defined operators and for the identity operator and we determine those classes of operators which admit finite-dimensional Korovkin subspaces. Finally, we give a Korovkin-type theorem for continuous positive...

Lattices with real numbers as additive operators

W. Holsztyński

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CONTENTSIntroduction............................... 5Paragraph 1............................... 6Paragraph 2............................... 13Paragraph 3............................... 21Paragraph 4............................... 27Paragraph 5............................... 36Paragraph 6............................... 42Paragraph 7............................... 52Paragraph 8............................... 60Paragraph 9............................... 70References....................................

Backward extensions of hyperexpansive operators

Zenon J. Jabłoński, Il Bong Jung, Jan Stochel (2006)

Studia Mathematica

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The concept of k-step full backward extension for subnormal operators is adapted to the context of completely hyperexpansive operators. The question of existence of k-step full backward extension is solved within this class of operators with the help of an operator version of the Levy-Khinchin formula. Some new phenomena in comparison with subnormal operators are found and related classes of operators are discussed as well.

Once more on positive commutators

Roman Drnovšek (2012)

Studia Mathematica

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Let A and B be bounded operators on a Banach lattice E such that the commutator C = AB - BA and the product BA are positive operators. If the product AB is a power-compact operator, then C is a quasi-nilpotent operator having a triangularizing chain of closed ideals of E. This answers an open question posed by Bračič et al. [Positivity 14 (2010)], where the study of positive commutators of positive operators was initiated.