𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the spectral radius of positive operators on Banach sequence spaces

✍ Scribed by Roman Drnovšek; Aljoša Peperko

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
144 KB
Volume
433
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

Let K 1 , . . . , K n be (infinite) non-negative matrices that define operators on a Banach sequence space. Given a function f : ) of n variables, we define a nonnegative matrix f (K 1 , . . . , K n ) and consider the inequality

where r denotes the spectral radius. We find the largest function f for which this inequality holds for all K 1 , . . . , K n . We also obtain an infinite-dimensional extension of the result of Cohen asserting that the spectral radius is a convex function of the diagonal entries of a non-negative matrix.

📜 SIMILAR VOLUMES

On Operators Acting on Convergent Sequen
On Operators Acting on Convergent Sequences in Banach Spaces
✍ K. Peter Cass 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 335 KB 👁 1 views

Our concern is to find a representation theorem for operators in B ( c ( X ) , c ( Y ) ) where S and Y are Banach spaces with Y containing an isomorphic copy of Q. CASS and GAO [l] obtained a iq,resentation theorem that always applies if Y does not contain an isomorphic copy of Q. MADDOX [:$I, MELVI