کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6416840 1336872 2012 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Completely bounded norms of right module maps
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Completely bounded norms of right module maps
چکیده انگلیسی

It is well-known that if T is a Dm-Dn bimodule map on the m × n complex matrices, then T is a Schur multiplier and ‖T‖cb=‖T‖. If n = 2 and T is merely assumed to be a right D2-module map, then we show that ‖T‖cb=‖T‖. However, this property fails if m ⩾ 2 and n ⩾ 3. For m ⩾ 2 and n = 3, 4 or n ⩾ m2 we give examples of maps T attaining the supremumC(m,n)=supT‖cb:Ta rightDn-module map onMm,nwith‖T‖≤1},we show that C(m,m2)=m and succeed in finding sharp results for C(m, n) in certain other cases. As a consequence, if H is an infinite-dimensional Hilbert space and D is a masa in B(H), then there is a bounded right D-module map on K(H) which is not completely bounded.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 436, Issue 5, 1 March 2012, Pages 1406-1424
نویسندگان
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