publication . Preprint . 2014

Minimal and Maximal Operator Space Structures on Banach Spaces

P., Vinod Kumar; Balasubramani, M. S.;
Open Access English
  • Published: 18 Nov 2014
Abstract
Given a Banach space $X$, there are many operator space structures possible on $X$, which all have $X$ as their first matrix level. Blecher and Paulsen identified two extreme operator space structures on $X$, namely $Min(X)$ and $Max(X)$ which represents respectively, the smallest and the largest operator space structures admissible on $X$. In this note, we consider the subspace and the quotient space structure of minimal and maximal operator spaces.
Subjects
arXiv: Mathematics::Functional Analysis
free text keywords: Mathematics - Operator Algebras, 46L07, 47L25
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of E ≤ n2. By assumption, E is minimal and by using the Hahn-Banach [3] D. Blecher and C. Le Merdy, 'Operator Algebras and their modules, An operator space

approach', (London Mathematical Society Monographs, Oxford University Press, 2004) [4] D. Blecher and V. Paulsen, 'Tensor products of operator spaces',J. Funct. Anal. 99

(1991) 262-292. [5] E. Effros and Z.-J. Ruan, Operator Spaces (London Math. Soc. Monographs. New Series,

Oxford University Press, 2000). [6] M. Junge , Factorization theory for spaces of operators. Habilitationsschrift,Universitat

Kiel, (1996). [7] U. Haggerup and G. Pisier 'Bounded linear operators between C *-algebras' Duke Math.

J. 71 ( 1993) 889-925. [8] T. Oikhberg, 'Subspaces of Maximal Operator Spaces', Integr. equ. oper. theory 48

(2004) 81-102. [9] T. Oikhberg , 'The complete isomorphism class of an operator space', Proc. Amer.

Math. Soc. 135 (12) (2007) 3943-3948. [10] V. Paulsen, 'Representation of function algebras, Abstract operator spaces and Banach

space geometry', J. Funct. Anal. 109 (1992) 113-129. [11] V. Paulsen, 'The maximal operator space of a normed space', Proc. Edinburgh. Math.

Soc. 39 (1996) 309-323. [12] G. Pisier 'Non-commutative vector valued Lp-spaces and completely p-summing maps',

Ast´erisque ,Soc. Math. France. 247 (1998) 1-131. [13] G. Pisier, Introduction to operator space theory (Cambridge University Press, 2003). [14] E. Ricard, 'A tensor norm for Q-spaces', J. Operator theory 48 (2002) 431-445. [15] Vinod Kumar P. and M.S. Balasubramani, 'Submaximal Operator Space Structures on

Banach Spaces', Oper. Matrices, 7( 3), (2013), 723-732. [16] Vinod Kumar P. and M.S. Balasubramani, 'A Note on Submaximal Operator Space

Structures', arXiv:1212.2315v1 [math.OA] 11 Dec 2012. [17] Z.-J. Ruan, 'Subspaces of C∗-algebras', J. Funct. Anal. 76 (1988) 217-230.

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