On the Lattice Properties of Almost L-Weakly and Almost M-Weakly Compact Operators

We establish the domination property and some lattice approximation properties for almost L-weakly and almost M-weakly compact operators. Then, we consider the linear span of positive almost L-weakly (resp., almost M-weakly) compact operators and give results about when they form a Banach lattice and have an order continuous norm.

Convex semigroups on $$L^p$$-like spaces

In this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having $$L^p$$ L p -spaces in mind as a typical application. We show that the basic results from linear $$C_0$$ C 0 -semigroup theory extend to the convex case. We prove that the generator of a convex $$C_0$$ C 0 -semigroup is closed and uniquely determines the semigroup whenever the domain is dense. Moreover, the domain of the generator is invariant under the semigroup, a result that leads to the well-posedness of the related Cauchy problem. In a last step, we provide conditions for the existence and strong continuity of semigroup envelopes for families of $$C_0$$ C 0 -semigroups. The results are discussed in several examples such as semilinear heat equations and nonlinear integro-differential equations.

Kadec–Klee properties of Orlicz–Lorentz sequence spaces equipped with the Orlicz norm

The necessary and sufficient conditions for both the Kadec–Klee property as well as the Kadec–Klee property with respect to the coordinatewise convergence in Orlicz–Lorentz sequence spaces equipped with the Orlicz norm and generated by arbitrary Orlicz functions as well as any non-increasing weight sequences are given. Moreover, for their subspaces of elements with an order continuous norm the full characterization of the Kadec–Klee property with respect to the coordinatewise convergence is presented. Some tools useful in the proofs of the main results are also provided.

Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions

Extending a result of Mashreghi and Ransford, we prove that every complex separable infinite-dimensional Fréchet space with a continuous norm is isomorphic to a space continuously included in a space of holomorphic functions on the unit disc or the complex plane, which contains the polynomials as a dense subspace. As a consequence, we deduce the existence of nuclear Fréchet spaces of holomorphic functions without the bounded approximation.

M-embedded symmetric operator spaces and the derivation problem

Let ℳ be a semifinite von Neumann algebra with a faithful semifinite normal trace τ. Assume that E(0, ∞) is an M-embedded fully symmetric function space having order continuous norm and is not a superset of the set of all bounded vanishing functions on (0, ∞). In this paper, we prove that the corresponding operator space E(ℳ, τ) is also M-embedded. It extends earlier results by Werner [48, Proposition 4∙1] from the particular case of symmetric ideals of bounded operators on a separable Hilbert space to the case of symmetric spaces (consisting of possibly unbounded operators) on an arbitrary semifinite von Neumann algebra. Several applications are given, e.g., the derivation problem for noncommutative Lorentz spaces ℒp,1(ℳ, τ), 1 < p < ∞, has a positive answer.

The Modulus of Nearly Uniform Smoothness in Orlicz Sequence Spaces

It is well known that the modulus of nearly uniform smoothness related with the fixed point property is important in Banach spaces. In this paper, we prove that the modulus of nearly uniform smoothness in Köthe sequence spaces without absolutely continuous norm is ΓX(t)=t. Meanwhile, the formula of the modulus of nearly uniform smoothness in Orlicz sequence spaces equipped with the Luxemburg norm is given. As a corollary, we get a criterion for nearly uniform smoothness of Orlicz sequence spaces equipped with the Luxemburg norm. Finally, the equivalent conditions of R(a,l(Φ))<1+a and RW(a,l(Φ))<1+a are given.

Leading the Change with Six Images of a Change Leader

Change is constant, and it is a continuous norm. It has even been said that, “to refuse to change is to be left behind” (anonymous). While difficult, this is still something that both individuals and organizations must cope with. The world is constantly changing, which explains why individuals and organizations that are open to change continue to survive. Many researchers have argued that an organization may only achieve a successful change when there is effective leadership. Effective leaders are those who understand when to change and how much to change. The purpose of this paper is to reiterate the importance of leadership in implementing a successful and transformational change in an organization. It will further explore a body of literature that supports and identifies roles leaders take on in the change management process.

THE CESÀRO OPERATOR IN THE FRÉCHET SPACES ℓp+ AND Lp−

The classical spaces ℓp+, 1 ≤ p < ∞, and Lp−, 1<p ≤ ∞, are countably normed, reflexive Fréchet spaces in which the Cesàro operator C acts continuously. A detailed investigation is made of various operator theoretic properties of C (e.g., spectrum, point spectrum, mean ergodicity) as well as certain aspects concerning the dynamics of C (e.g., hypercyclic, supercyclic, chaos). This complements the results of [3, 4], where C was studied in the spaces ℂℕ, Lploc(ℝ+) for 1 < p < ∞ and C(ℝ+), which belong to a very different collection of Fréchet spaces, called quojections; these are automatically Banach spaces whenever they admit a continuous norm.

Norm Evolution a Matter of Conformity and Contestedness: South Africa and the Responsibility to Protect

Research on international norms has been thriving for decades, most prominently exploring processes of norm creation and compliance. Yet the mainstream literature has paid scant attention to the issue of continuous norm evolution beyond a norm’s emergence. In this article we aim at framing the wider context in which norm evolution is taking place. We identify two antipodes: conformity and contestedness between which norms continue to evolve. We will exemplify this by analysing the norm of the responsibility to protect (R2P) through general usage and South Africa’s response. The article finds that norm evolution is mostly influenced by conformity with some measure of contestedness as a motor for change.