Department of Mathematics
u tau-convergence in locally solid vector lattices
Dabboorasad, Y. A.; Emelyanov, Eduard; Marabeh, M. A. A. (Springer Science and Business Media LLC, 2018-09-01)
Let be a net in a locally solid vector lattice ; we say that is unbounded -convergent to a vector if for all . In this paper, we study general properties of unbounded -convergence (shortly -convergence). -convergence gener...
Komls properties in Banach lattices
Emelyanov, Eduard; ERKURŞUN ÖZCAN, NAZİFE; Gorokhova, S. G. (2018-08-01)
Several Komls like properties in Banach lattices are investigated. We prove that C(K) fails the -pre-Komls property, assuming that the compact Hausdorff space K has a nonempty separable open subset U without isolated point...
um-Topology in multi-normed vector lattices
Dabboorasad, Y. A.; Emelyanov, Eduard; Marabeh, M. A. A. (2018-04-01)
Let be a separating family of lattice seminorms on a vector lattice X, then is called a multi-normed vector lattice (or MNVL). We write if for all . A net in an MNVL is said to be unbounded m-convergent (or um-convergent) ...
Archimedean Cones in Vector Spaces
Emelyanov, Eduard (2017-01-01)
In the case of an ordered vector space (briefly, OVS) with an order unit, the Archimedeanization method was recently developed by Paulsen and Tomforde [4]. We present a general version of the Archimedeanization which cover...
Nonstandard hulls of ordered vector spaces
Emelyanov, Eduard; Gul, Hasan (2016-06-01)
This paper undertakes the investigation of ordered vector spaces by applying nonstandard analysis. We introduce and study two types of nonstandard hulls of ordered vector spaces. Norm-nonstandard hulls of ordered Banach sp...
On quasi-compactness of operator nets on Banach spaces
Emelyanov, Eduard (Institute of Mathematics, Polish Academy of Sciences, 2011-01-01)
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(lam...
Lotz-Rabiger's nets of Markov operators in L-1-spaces
Emelyanov, Eduard; Erkursun, Nazife (Elsevier BV, 2010-11-15)
The Lotz-Rabiger nets (LR-nets) introduced in Rabiger (1993) [18] under the name M-nets provide an appropriate setting for investigation various mean ergodic theorems in Banach spaces. In the present paper we prove several...
An extension of Sine's counterexample
Emelyanov, Eduard; Erkursun, Nazife (Springer Science and Business Media LLC, 2009-02-01)
We generalize Sine's example [3] of a positive contraction in a C(K)-space which is mean ergodic, but its square is not.
Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups
Emelyanov, Eduard (Birkhäuser Verlag 2007, 2007-01-01)
Mean ergodicity of positive operators in KB-space
Alpay, S.; Binhadjah, A.; Emelyanov, Eduard; Ercan, Z. (Elsevier BV, 2006-11-01)
We prove that any positive power bounded operator T in a KB-space E which satisfies
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