Generalized open mapping theorems for bilinear maps, with an application to operator algebras
Proc. Amer. Math. Soc., 104 (1988), 106-110.
1991 Mathematics Subject Classification: primary 46A30; secondary 47D35
Cohen  gave an example of a surjective bilinear mapping between Banach spaces
which was not open, and Horowitz  gave a much simpler example. We build on Horowitz's
example to produce a similar result for bilinear mappings such that every element of the target space
is a linear combination of n elements of the range. An immediate application is that
Bercovici's construction  of an operator algebra with property (A1) but not
(A1(r)) can be extended to achieve property (A1/n) without
- H. Bercovici, `Note on property (A1)', Linear Algebra Appl., 91
- P. J. Cohen, `A counterexample to the closed graph theorem for bilinear maps',
J. Functional Analysis, 16 (1974), 235-239.
- C. Horowitz, `An elementary counterexample to the open mapping principle for bilinear maps',
Proc. Amer. Math. Soc., 53 (1975), 293-294.
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