Factorization and reflexivity on Fock spaces |
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Authors: | Alvaro Arias Gelu Popescu |
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Institution: | (1) Division of Mathematics, Computer Science and Statistics, The University of Texas at San Antonio, 78249 San Antonio, TX, USA;(2) Division of Mathematics, Computer Science and Statistics, The University of Texas at San Antonio, 78249 San Antonio, TX, USA |
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Abstract: | The framework of the paper is that of the full Fock space
and the Banach algebraF
which can be viewed as non-commutative analogues of the Hardy spacesH
2 andH
respectively.An inner-outer factorization for any element in
as well as characterization of invertible elements inF
are obtained. We also give a complete characterization of invariant subspaces for the left creation operatorsS
1
,..., S
n
of
. This enables us to show that every weakly (strongly) closed unital subalgebra of { (S
1
,..., S
n
) ![phgr](/content/j5j420q241663120/xxlarge966.gif) F
} is reflexive, extending in this way the classical result of Sarason S]. Some properties of inner and outer functions and many examples are also considered.The first author was supported in part by NSF DMS 93-21369 1991Mathematics Subject Classification. Primary 47D25, Secondary 32A35, 47A67. |
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Keywords: | |
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