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Direct limit of matrix order unit spaces

J. V. Ramani; Anil K. Karn; Sunil Yadav — 2008

Colloquium Mathematicae

The notion of ℱ-approximate order unit norm for ordered ℱ-bimodules is introduced and characterized in terms of order-theoretic and geometric concepts. Using this notion, we characterize the inductive limit of matrix order unit spaces.

Direct limit of matricially Riesz normed spaces

J. V. Ramani; Anil Kumar Karn; Sunil Yadav — 2006

Commentationes Mathematicae Universitatis Carolinae

In this paper, the $ℱ$ -Riesz norm for ordered $ℱ$ -bimodules is introduced and characterized in terms of order theoretic and geometric concepts. Using this notion, $ℱ$ -Riesz normed bimodules are introduced and characterized as the inductive limits of matricially Riesz normed spaces.

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