Main Article Content
Norm One Projections on Banach Spaces
Abstract
This note deals with a small but an important observation
of hermitian operators on Banach spaces. It is known that if A is a complex
Banach space, B(A) is the set of all operators on A, and H(B(A)) is the set
of all hermitian operators then B(A) = H(B(A)) + iH(B(A)) implies that A is
a Hilbert space. We give a converse of this using norm one projections on A.
Mathematics Subject Classification (2000): 46H05, 46J10, 4715, 47B48.
Keywords: projections, Banach, banach space, ultra product of an operator,
hermitian operators, direct sum of spaces, norm one, Banach algebra, continuous
functions, function algebras, normal operators, operators, Brown-McCoy, Brown-McCoy
radical, radical, non-0-symmetric near-ring, near-rings, near rings, semisimple,
identities, radical classes, invariant ideals, ideals, Banach spaces
Quaestiones Mathematicaes 24 (4) 2001, 491–492
of hermitian operators on Banach spaces. It is known that if A is a complex
Banach space, B(A) is the set of all operators on A, and H(B(A)) is the set
of all hermitian operators then B(A) = H(B(A)) + iH(B(A)) implies that A is
a Hilbert space. We give a converse of this using norm one projections on A.
Mathematics Subject Classification (2000): 46H05, 46J10, 4715, 47B48.
Keywords: projections, Banach, banach space, ultra product of an operator,
hermitian operators, direct sum of spaces, norm one, Banach algebra, continuous
functions, function algebras, normal operators, operators, Brown-McCoy, Brown-McCoy
radical, radical, non-0-symmetric near-ring, near-rings, near rings, semisimple,
identities, radical classes, invariant ideals, ideals, Banach spaces
Quaestiones Mathematicaes 24 (4) 2001, 491–492
