Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 12, Number 2 (2018), 314-330.
Lower and upper local uniform -monotonicity in symmetric spaces
Using the local approach to the global structure of a symmetric space , we establish a relationship between strict -monotonicity, lower (resp., upper) local uniform -monotonicity, order continuity, and the Kadec–Klee property for global convergence in measure. We also answer the question: Under which condition does upper local uniform -monotonicity coincide with upper local uniform monotonicity? Finally, we present a correlation between -order continuity and lower local uniform -monotonicity in a symmetric space under some additional assumptions on .
Banach J. Math. Anal., Volume 12, Number 2 (2018), 314-330.
Received: 14 March 2017
Accepted: 12 April 2017
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 46B20: Geometry and structure of normed linear spaces 46B42: Banach lattices [See also 46A40, 46B40]
Ciesielski, Maciej. Lower and upper local uniform $K$ -monotonicity in symmetric spaces. Banach J. Math. Anal. 12 (2018), no. 2, 314--330. doi:10.1215/17358787-2017-0047. https://projecteuclid.org/euclid.bjma/1513674116