Vol. 42, No. 2, 1972

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The spectrum of certain lower triangular matrices as operators on the lp spaces

James D. Stafney

Vol. 42 (1972), No. 2, 515–525
Abstract

In this paper we compute the spectrum of the lower triangular matrices Aa = (em,n), where cmn = (n + 1)a(m + 1)a+1, m n 0,a is real and the corresponding operator on lp is bounded (see 4.1). This result and other lemmas are used to determine the spectrum of lower triangular matrices p(n)lq(m), m n 0 as operators on lp where p is a monic polynomial of degree a,q is a monic polynomial of degree a + 1 and q(m)0 for m = 0,1, . The spectrum is the diagonal together with the set Cap 1+1 when a p1 + 1 > 0, where Cb = {λ;|λ (2b)1|(2b)1} (see 4.3).

Mathematical Subject Classification 2000
Primary: 47A10
Secondary: 47B35
Milestones
Received: 1 April 1971
Revised: 20 December 1971
Published: 1 August 1972
Authors
James D. Stafney