On the geometry of the unit ball of unitary matrix spaces

1981 ◽  
Vol 4 (2) ◽  
pp. 151-171 ◽  
Author(s):  
Jonathan Arazy
Keyword(s):  
Unit Ball ◽  
Unitary Matrix ◽  
Matrix Spaces

Local uniform and uniform convexity of non-commutative symmetric spaces of measurable operators

1992 ◽  
Vol 111 (2) ◽  
pp. 355-368 ◽  
Author(s):  
Vladimir I. Chilin ◽  
Andrei V. Krygin ◽  
Pheodor A. Sukochev
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Symmetric Spaces ◽  
Compact Operators ◽  
Uniform Convexity ◽  
Unitary Matrix ◽  
Matrix Space ◽  
Measurable Operators ◽  
Unitary Matrix Space ◽  
Matrix Spaces

Let E be a separable symmetric sequence space, and let CE be the unitary matrix space associated with E, i.e. the Banach space of all compact operators x on l2 so that s(x) E, with the norm , where are the s-numbers of x. One of the interesting subjects in the theory of the unitary matrix spaces is the clarification of correlation between the geometric properties of the spaces E and CE. A series of results in this direction related with the notions of type, cotype and uniform convexity of the spaces CE has been already obtained (see 13).

On p-convexity and q-concavity of unitary matrix spaces

1985 ◽  
Vol 8 (3) ◽  
pp. 295-313 ◽  
Author(s):  
Jonathan Arazy ◽  
Pei-Kee Lin
Keyword(s):  
Unitary Matrix ◽  
Matrix Spaces

Holomorphically embedded discs with rapidly growing area

1999 ◽  
Vol 129 (2) ◽  
pp. 343-349
Author(s):  
Josip Globevnik
Keyword(s):  
Unit Ball ◽  
Open Unit ◽  
Open Unit Ball

It is shown that if V is a closed submanifold of the open unit ball of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ 1. It is also shown that if V is a closed submanifold of ℂ2 biholomorphically equivalent to a disc, then the area of V ∩ r can grow arbitrarily rapidly as r ↗ ∞.

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