Quasi-Norms for a Double Sequence
Copyright policy )Quasi-Norms for a Double Sequence
Summary: The purpose of this note is to define and characterize different kinds of quasi-norms for a double sequence obtained by generalizing the \(l^p\)-norm. In particular, we focus on two weak \(l^p\)-norms: successive weak \(l^p\)-norm and standard weak \(l^p\)-norm. We give upper and lower bounds of the ratio of a successive weak \(l^p\)-norm to a standard weak \(l^p\)-norm for any double sequence.
- Tohoku University Japan
- Tokyo Metropolitan University Japan
Lorentz norm, Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), weak \(l^p\)-norms, Banach sequence spaces, quasi-norms
Lorentz norm, Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), weak \(l^p\)-norms, Banach sequence spaces, quasi-norms
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