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- W2081616941 abstract "Next suppose His a separable real or complex Hilbert space, (e,,} an orthonormal basis, and let P, be the orthogonal projection of H onto the subspace H, spanned by {eI, . . . , e,}. Let B(H) denote the Banach algebra of bounded operators on H (with 11 II,.,, the usual norm, defined by lAll oD = Sup{ ll~xll Ix E D) w h ere D is the closed unit ball in H), B(HJ the finite dimensional subalgebra of operators which map H, into itself and are zero on Hi and let Q, denote the projection of B(H) onto B(H,J given by Q,,(A) = P,,.4P”. Let GL(H) denote the group of units of B(H), and let GL(n) denote the subgroup consisting of invertible operators of the form Z + A where Z is the identity and A E B(H,J. Finally let GL(co) = lim GL(n) (the homotopy groups of GL(co) are given by the Bott periodic@ theorems [z" @default.
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- W2081616941 date "1965-05-01" @default.
- W2081616941 modified "2023-09-26" @default.
- W2081616941 title "On the homotopy type of certain groups of operators" @default.
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