The adjoint of a positive semigroup
The -weak compactness of weak Banach-Saks operators
We characterize Banach lattices on which every weak Banach-Saks operator is b-weakly compact.
The Banach lattice C[0,1] is super d-rigid
The following properties of C[0,1] are proved here. Let T: C[0,1] → Y be a disjointness preserving bijection onto an arbitrary vector lattice Y. Then the inverse operator is also disjointness preserving, the operator T is regular, and the vector lattice Y is order isomorphic to C[0,1]. In particular if Y is a normed lattice, then T is also automatically norm continuous. A major step needed for proving these properties is provided by Theorem 3.1 asserting that T satisfies some technical condition...
The Components of a Positive Operator.
The distance from a point to a cone in a Hilbert space.
The ideal property of tensor products of Banach lattices with applications to the local structure of spaces of absolutely summing operators
The injective hull of an archimedean f-algebra
The mapping problem for well-behaved convolutions
The linear modulus of an integral operator
The Modulus of a Weakly Compact Operator.
The order -complete vector lattice of AM-compact operators
We establish necessary and sufficient conditions under which the linear span of positive AM-compact operators (in the sense of Fremlin) from a Banach lattice into a Banach lattice is an order -complete vector lattice.
The Peripheral Point Spectrum of Schwarz Operators on C*-Algebras.
The Perron-Frobenius theorem in relative spectral theory.
The Projection onto the Center of Operators in a Banach Lattice.
The uniform zero-two law for positive operators in Banach lattices
The weak compactness of almost Dunford-Pettis operators
We characterize Banach lattices on which every positive almost Dunford-Pettis operator is weakly compact.
Théorèmes de factorisation dans les espaces réticules
Topologische Nilpotenz irreduzibler Operatoren.
Trace inequalities for spaces in spectral duality
Let (A,e) and (V,K) be an order-unit space and a base-norm space in spectral duality, as in noncommutative spectral theory of Alfsen and Shultz. Let t be a norm lower semicontinuous trace on A, and let φ be a nonnegative convex function on ℝ. It is shown that the mapping a → t(φ(a)) is convex on A. Moreover, the mapping is shown to be nondecreasing if so is φ. Some other similar statements concerning traces and real-valued functions are also obtained.