Compact-like operators in lattice-nonmed. spaces

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AYDIN A., EMELYANOV E., ERKURŞUN ÖZCAN N., Marabeh M. A. A.

INDAGATIONES MATHEMATICAE-NEW SERIES, cilt.29, sa.2, ss.633-656, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.indag.2017.11.002
  • Dergi Adı: INDAGATIONES MATHEMATICAE-NEW SERIES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.633-656
  • Anahtar Kelimeler: Compact operator, Vector lattice, Lattice-normed space, Lattice-normed vector lattice, up-convergence, Mixed-normed space, CONVERGENCE
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

A linear operator T between two lattice-normed spaces is said to be p-compact if, for any p-bounded net x(alpha),,the net Tx(alpha) has a p-convergent subnet. p-Compact operators generalize several known classes of operators such as compact, weakly compact, order weakly compact, AM-compact operators, etc. Similar to M-weakly and L-weakly compact operatois, we define p-M-weakly and p-L-weakly compact operators and study some of their properties. We also study up-continuous and up"compact operators between lattice nonmed vector lattices. (C) 2017 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.