Approximate point spectrum of a weighted shift

摘要: Notation. If T is a Hilbert space operator, let A(T) denote its spectrum, fl(T) approximate point flo(T) r(T) compression m(T) lower bound (i.e., inf{ lTxll/llxll: x7&0}), and spectral radius. Let i(T) supn m(Tn)l"n, which equals limn m(Tn)1"n. R weighted right shift on 11, defined by Ren=snen +I , where (en) an orthonormal basis of 12, n = 1, 2, .... L adjoint, left shift. B two-sided Ben=sSnen+1 n=0, ? .. ., here being 12. has purely nonzero weights (sn), then