A counterexample to a conjecture of Matsaev

作者：Drury S W^*

来源：Linear Algebra and Its Applications, 2011, 435(2): 323-329.

DOI：10.1016/j.laa.2011.01.022

• Matsaev's conjecture
• Operator
• l(p)-spaces
• Symbolic calculus
• L-p multiplier

We present an effective algorithm for estimating the norm of an operator mapping a low-dimensional l(p) space to a Banach space with an easily computable norm. We use that algorithm to show that Matsaev's proposed extension of the inequality of John von Neumann is false in case p = 4. Matsaev conjectured that for every contraction Ton L-P (1 < p < infinity) one has for any polynomial P
parallel to P(T)parallel to(LP -> LP) <= parallel to P(S)parallel to(lp(Z+)-> lP(Z+)),
where S is the unilateral shift.

• 出版日期2011-7-15