THE CANONICAL HALF-NORM, DUAL HALF-NORMS, AND MONOTONIC NORMS

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概要

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• Let (B, B_ +, \left// · \right//) be an ordered Banach space and define the canonical half-normN(a) = \inf \left{ {\left// {a + b} \right//;b \in {B_ + }} \right}We prove that N(a) = \left// a \right// for a \in {B_ + } if, and only if, the norm is (1-) monotonic on B, andN(a) = \inf \left{ {\left// b \right//;b \in {B_ + }, b - a \in {B_ + }} \right}if, and only if, the dual norm is (1-)monotonic on {B<SUP>*</SUP>}. Subsequently we examine the canonical half-norm in the dual and prove that it coincides with the dual of the canonical half-norm.

• 東北大学大学院理学研究科数学専攻の論文

著者

• Robinson Derek

  Department Of Mathematics Institute Of Advanced Studies

• Robinson Derek

  Department Of Mathematics Institute Of Advanced Studies Australian National University

• YAMAMURO SADAYUKI

  DEPARTMENT OF MATHEMATICS INSTITUTE OF ADVANCED STUDIES AUSTRALIAN NATIONAL UNIVERSITY

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