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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,...
CONTENTSIntroduction................................................. 51. Basic concepts and terminology................ 92. Generalized intertwining maps................... 123. Commutative regular algebras................... 184. C*-algebras.................................................... 255. Algebras of differentiable functions............ 31Bibliography........................................................ 51
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