Geodesic
Closed range multipliers and generalized inverses
Studia Mathematica, Tome 107 (1993) no. 2, pp. 127-135

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-107-2-127-135

K. B. Laursen 1 ;  1

1 
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K. B. Laursen;  . Closed range multipliers and generalized inverses. Studia Mathematica, Tome 107 (1993) no. 2, pp. 127-135. doi: 10.4064/sm-107-2-127-135

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