Closed range multipliers and generalized inverses
Laursen, K. ; Mbekhta, M.
Studia Mathematica, Tome 104 (1993), p. 127-135 / Harvested from The Polish Digital Mathematics Library
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Conditions involving closed range of multipliers on general Banach algebras are studied. Numerous conditions equivalent to a splitting A = TA ⊕ kerT are listed, for a multiplier T defined on the Banach algebra A. For instance, it is shown that TA ⊕ kerT = A if and only if there is a commuting operator S for which T = TST and S = STS, that this is the case if and only if such S may be taken to be a multiplier, and that these conditions are also equivalent to the existence of a factorization T = PB, where P is an idempotent and B an invertible multiplier. The latter condition establishes a connection to a famous problem of harmonic analysis.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:216025 
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     year = {1993},
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Laursen, K.; Mbekhta, M. Closed range multipliers and generalized inverses. Studia Mathematica, Tome 104 (1993) pp. 127-135. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv107i2p127bwm/

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