Cyclic behavior of linear fractional composition operators.
E. A. Gallardo-Gutiérrez, A. Montes-Rodríguez (2001)
Extracta Mathematicae
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E. A. Gallardo-Gutiérrez, A. Montes-Rodríguez (2001)
Extracta Mathematicae
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Pei Wu (1994)
Banach Center Publications
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This is a survey paper on additive combinations of certain special-type operators on a Hilbert space. We consider (finite) linear combinations, sums, convex combinations and/or averages of operators from the classes of diagonal operators, unitary operators, isometries, projections, symmetries, idempotents, square-zero operators, nilpotent operators, quasinilpotent operators, involutions, commutators, self-commutators, norm-attaining operators, numerical-radius-attaining operators, irreducible...
Rashid, M.H.M., Noorani, M.S.M., Saari, A.S. (2008)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Fernando León-Saavedra, Vladimír Müller (2006)
Studia Mathematica
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A sequence (Tₙ) of bounded linear operators between Banach spaces X,Y is said to be hypercyclic if there exists a vector x ∈ X such that the orbit Tₙx is dense in Y. The paper gives a survey of various conditions that imply the hypercyclicity of (Tₙ) and studies relations among them. The particular case of X = Y and mutually commuting operators Tₙ is analyzed. This includes the most interesting cases (Tⁿ) and (λₙTⁿ) where T is a fixed operator and λₙ are complex numbers. We also study...
Svetlana Mincheva (2000)
Banach Center Publications
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Convolutional representations of the commutant of the partial integration operators in the space of continuous functions in a rectangle are found. Necessary and sufficient conditions are obtained for two types of representing functions, to be the operators in the commutant continuous automorphisms. It is shown that these conditions are equivalent to the requirement that the considered representing functions be joint cyclic elements of the partial integration operators.
Vladimír Müller (1994)
Banach Center Publications
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Jaroslav Zemánek (1994)
Banach Center Publications
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Mecheri, Salah (2009)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
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Ana Pradera, Enric Trillas (2006)
Mathware and Soft Computing
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This paper investigates the satisfaction of the Non-Contradiction (NC) and Excluded-Middle (EM) laws within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given strong negation, as well as for those satisfying them w.r.t. any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators.
Gyan Prakash Tripathi (2009)
Matematički Vesnik
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Karl-Goswin Grosse-Erdmann (2003)
RACSAM
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In these notes we report on recent progress in the theory of hypercyclic and chaotic operators. Our discussion will be guided by the following fundamental problems: How do we recognize hypercyclic operators? How many vectors are hypercyclic? How many operators are hypercyclic? How big can non-dense orbits be?