In this paper we consider the question when an upward directed set of positive ideal-triangularizable operators on a Banach lattice is (simultaneously) ideal-triangularizable. We prove that a majorized upward directed set of ideal-triangularizable positive operators, which are compact or abstract integral operators is ideal-triangularizable. We also prove that a finite subset of an additive sem...

We present two applications Ball’s extension theorem. First we observe that Ball’s extension theorem, together with the recent solution of Ball’s Markov type 2 problem due to Naor, Peres, Schramm and Sheffilield, imply a generalization, and an alternative proof of, the Johnson-Lindenstrauss extension theorem. Secondly, we prove that the distortion required to embed the integer lattice {0, 1, . ...

Abstract. The process of recombination in population genetics, in its deterministic limit, leads to a nonlinear ODE in the Banach space of finite measures on a locally compact product space. It has an embedding into a larger family of nonlinear ODEs that permits a systematic analysis with lattice-theoretic methods for general partitions of finite sets. We discuss this type of system, reduce it ...

In this note the propertiesof the peripheral spectrum of a nonnegativelinear operator A for which the spectral radius is a pole of its resolvent in a complex Banach lattice are studied. It is shown, e.g., that the peripheral spectrum of a natural quotient operator is always fully cyclic. We describe when the nonnegative eigenvectors corresponding to the spectral radius r span the kernel Nr , A....

and Applied Analysis 3 In fact, for n 1, using the fact that P is normal, we have ∥ ∥ ∥A u0 −Au0 ∥ ∥ ∥ ≤ N‖L Au0 − u0 ‖. 2.3 Suppose that 2.2 is true when n k then when n k 1, we obtain ∥ ∥ ∥A 2 u0 −An 1 u0 ∥ ∥ ∥ ∥ ∥ ∥A ( A 1 u0 ) −A A u0 ∥ ∥ ∥ ≤ N ∥ ∥ ∥L ( A 1 u0 −An u0 )∥ ∥ ∥ ≤ N ∥ ∥ ∥L 1 Au0 − u0 ∥ ∥ ∥. 2.4 For any m,n ∈ N,m > n, since P is normal cone, we have ‖A u0 −An u0 ‖ ∥ ∥ ∥ ( A u0 −A...

 For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto  fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an o...

In this paper, we introduce and investigate new concepts of L-weakly M-weakly demicompact operators. Let E be a Banach lattice. An operator T : ? is called demicompact, if for every norm bounded sequence (xn) in BE such that {xn Txn, n N} an compact subset E, have {xn, E. Additionally, disjoint ?xn ?Txn? 0, ?xn? 0. (resp. M-weakly) operators generalize known classes which are We also elaborate ...