Compact-Like Operators in Lattice-Normed Spaces

2017/01/11 by Abdullah Aydın, Aydın, A., Eduard Emelyanov +5
Mathematics · #47B07 (Primary) 46B42 46A40 (Secondary) #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1701.03073

openalex publication_date 2017/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A linear operator T between two lattice-normed spaces is said to be p-compact if, for any p-bounded net x_α, the net Tx_α 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 operators, 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-normed vector lattices.

Related

• Compact-Like Operators in Vector Lattices Normed by Locally Solid Lattices
• Compact operators between lattice normed spaces
• Unbounded M-weakly and unbounded L-weakly compact operators
• A generalization of b-weakly compact operators
• order-norm continuous operators and order weakly compact operators