Equivalence relations and distances between Hilbert frames
نویسندگان
چکیده
منابع مشابه
Equivalence Relations and Distances between Hilbert Frames
We study some equivalency relations between Hilbert frames and closed subspaces of l2(I). We define also a distance between frames and we establish the geometric meaning of this metric. Finally we find the closest and respectively the nearest tight frame to a given frame.
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Assuming w is the only measurable cardinal, we prove: (i) Let ~ be an equivalence relation such that ~ = =z. for some logic L < L* satisfying Robinson's consistency theorem (with L* arbitrary); then there exists a strongest logic L+ « L* such that ~ = =/.+ ; in addition, L+ is countably compact if ~^= . (ii) Let ~ be an equivalence relation such that ~ = =/." for some logic L° satisfying Robins...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04826-1