Glasnik Matematicki, Vol. 48, No. 1 (2013), 97-102.

BOUNDED INJECTIVITY AND HAAGERUP TENSOR PRODUCT

Mohammad B. Asadi, Alireza Medghalchi and Hamed Nikpey

School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Enghelab Avenue, Tehran, Iran
and
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran
e-mail: mb.asadi@khayam.ut.ac.ir

Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani Avenue, Tehran, Iran
e-mail: a_medghalchi@saba.tmu.ac.ir

Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani Avenue, Tehran, Iran
e-mail: hamednikpey@gmail.com


Abstract.   In this paper, we prove that if V ⊆ B(H) is an injective operator system on a separable Hilbert space H, then V ⊗hW is b-injective for any operator system W if and only if V is finite dimensional.

2010 Mathematics Subject Classification.   47L25, 46L07.

Key words and phrases.   Operator system, injective operator space, bounded injective operator space, Haagerup tensor product.


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DOI: 10.3336/gm.48.1.09


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