A note on the sequence spacel (p v )

In this paper, the linear isometry of the sequence space l(pv) into itself is specified as the automorphism of l(pv) onto itself, when (pv) satisfies the conditions, (i) 0 < pv⩽ 1, (ii) 1 +d ⩽ pv ⩽ p < ∞,q < qv < 1+d/d,d > o When (pv) satisfies condition (ii),l (pv) andl (qv) are proved to be perfect spaces in the sense of Kothe and Toeplitz. A similar result connecting linear isometry and automorphism has been noted in the case of a non-normable complete linear metric space whose conjugate space is also determined.