Recently, Sharma and Sahu (Indian J. pure Appl. Math. 31 (2000), 185-96) claimed to have improved a theorem of Schu (J. Math. Anal. Appl. 158 (1991), 407-13) from Hilbert spaces to Banach spaces satisfying Opial's condition. These spaces include lp spaces, 1 <p < ∞, but exclude L p (1 < p < ∞, p ≠ 2). In a subsequent paper, the two authors, in collaboration with Bounias claimed to have extended this result to Banach spaces with property (U, λ, m+ 1, m), λ ε IR, m ε IN. These spaces include the Lp spaces, p ≥ 2. It is shown in this note that these claims are false. The proofs of all the results in these two papers of Sharma et al. are valid in Hubert spaces. The validity of the theorems in Lp (or lp), p > 2, has not been proved.
|Number of pages||3|
|Journal||Indian Journal of Pure and Applied Mathematics|
|Publication status||Published - May 1 2003|
All Science Journal Classification (ASJC) codes
- Applied Mathematics