On quasi-compactness of operator nets on Banach spaces

The paper introduces a notion of quasi-compact operator net on a Banach space. It is proved that quasi-compactness of a uniform Lotz-Rabiger net (T(lambda))(lambda) is equivalent to quasi-compactness of some operator T(lambda). We prove that strong convergence of a quasi-compact uniform Lotz-Rabiger net implies uniform convergence to a finite-rank projection. Precompactness of operator nets is also investigated.


Dosi, Anar (World Scientific Pub Co Pte Lt, 2011-04-01)
In this note we investigate quantizations of the weak topology associated with a pair of dual linear spaces. We prove that the weak topology admits only one quantization called the weak quantum topology, and that weakly matrix bounded sets are precisely the min-bounded sets with respect to any polynormed topology compatible with the given duality. The technique of this paper allows us to obtain an operator space proof of the noncommutative bipolar theorem.
KIRLAR, Barış Bülent; Cil, Melek (Walter de Gruyter GmbH, 2017-06-01)
In this paper, we propose a novel encryption scheme based on the concepts of the commutative law of the k-th order linear recurrences over the finite field F-q for k > 2. The proposed encryption scheme is an ephemeral-static, which is useful in situations like email where the recipient may not be online. The security of the proposed encryption scheme depends on the difficulty of solving some Linear Feedback Shift Register (LFSR) problems. It has also the property of semantic security. For k = 2, we propose ...
On entire rational maps of real surfaces
Ozan, Yıldıray (The Korean Mathematical Society, 2002-01-01)
In this paper, we define for a component X-0 of a nonsingular compact real algebraic surface X the complex genus of X-0, denoted by g(C)(X-0), and use this to prove the nonexistence of nonzero degree entire rational maps f : X-0 --> Y provided that g(C)(Y) > g(C)(X-0), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.
Geometric characterizations of existentially closed fields with operators
Pierce, D (Duke University Press, 2004-12-01)
This paper concerns the basic model-theory of fields of arbitrary characteristic with operators. Simplified geometric axioms are given for the model-companion of the theory of fields with a derivation. These axioms generalize to the case of several commuting derivations. Let a D-field be a field with a derivation or a difference-operator, called D. The theory of D-fields is companionable. The existentially closed D-fields can be characterized geometrically without distinguishing the two cases in which D can...
On the Krall-type polynomials on q-quadratic lattices
Alvarez-Nodarse, R.; Adiguzel, R. Sevinik (Elsevier BV, 2011-08-01)
In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. In particular, the q-Racah-Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard q-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed. (C) 2011 Royal Net...
Citation Formats
E. Emelyanov, “On quasi-compactness of operator nets on Banach spaces,” STUDIA MATHEMATICA, pp. 163–170, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37661.