Bounded, conservative, linear operators and the maximal group

E. P. Kelly, D. A. Hogan
1972 Proceedings of the American Mathematical Society  
Let V denote a Banach space over the reals, B[V] the bounded linear operators on K,/a linear functional defined on a complete subspace, (/), of V. A conservative operator is an element of the set ^,={T\TeB[V], T((f))c(f)}. In this setting this paper extends some of the results of a recent paper by Rhoades [Triangular summability methods and the boundary of the maximal group, Math. Z. 105 (1968), 284-290]. In this setting necessary and sufficient conditions are proven for Te&~f to be in the
more » ... al group of invertible elements, Jt'. Sufficient conditions are proven for Te3~f to be in the boundary, ¡B, of Jt'. It is proven that 38 is a multiplicative semigroup and if (/) is nontrivial, then Si is nonconvex. Two questions raised in the paper by Rhoades were answered.
doi:10.1090/s0002-9939-1972-0290136-3 fatcat:idcacjqt3bexvlxlwzrldx3g6e