论文信息 - Locating subsets of B(H) relative to seminorms inducing the strong-operator topology

Locating subsets of B(H) relative to seminorms inducing the strong-operator topology

Let H be a Hilbert space, andA an inhabited, bounded, convex subset ofB(H). We give a constructive proof thatA is weak-operator totally bounded if and only if it is located relative to a certain family of seminorms that induces the strong-operator topology onB(H).

Douglas S. Bridges | D. Bridges

[1] Per Martin-Löf,et al. Intuitionistic type theory , 1984, Studies in proof theory.

[2] Rance Cleaveland,et al. Implementing mathematics with the Nuprl proof development system , 1986 .

[3] F. Richman,et al. Varieties of Constructive Mathematics: CONSTRUCTIVE ALGEBRA , 1987 .

[4] 中野裕,et al. PX, a computational logic , 1988 .

[5] P. Aczel,et al. Notes on constructive set theory , 1997 .

[6] H. Ishihara. Locating subsets of a Hilbert space , 2000 .

[7] D. Bridges,et al. Computing infima on convex sets, with applications in Hilbert spaces , 2004 .

[8] Bas Spitters,et al. Constructive Results on Operator Algebras , 2005, J. Univers. Comput. Sci..

[9] D. Bridges,et al. Techniques of Constructive Analysis , 2006 .

[10] Ulrich Kohlenbach,et al. Applied Proof Theory - Proof Interpretations and their Use in Mathematics , 2008, Springer Monographs in Mathematics.

[11] S. Lindström,et al. Logicism, intuitionism, and formalism : what has become of them? , 2009 .

[12] H. Schwichtenberg. Program Extraction in Constructive Analysis , 2009 .

[13] E. Bishop. Foundations of Constructive Analysis , 2012 .