相关论文: Soft ideals and arithmetic mean ideals

In this manuscript the idea of soft convex structures is given and some of their properties are investigated. Also, soft convex sets, soft concave sets and soft convex hull operator are defined and their properties are studied. Moreover,…

We generalize an important class of Banach spaces, namely the $M$-embedded Banach spaces, to the non-commutative setting of operator spaces. The one-sided $M$-embedded operator spaces are the operator spaces which are one-sided $M$-ideals…

We use the notion of $\A$-compact sets, which are determined by a Banach operator ideal $\A$, to show that most classic results of certain approximation properties and several Banach operator ideals can be systematically studied under this…

For a topological space it is well-known that the associated closure and interior operators provide equivalent descriptions of set-theoretic topology; but it is not generally true in other categories, consequently it makes sense to define…

A proper ideal $I$ in a commutative ring with unity is called a $z^\circ$-ideal if for each $a$ in $I$, the intersection of all minimal prime ideals in $R$ which contain $a$ is contained in $I$. For any totally ordered field $F$ and a…

It has recently been argued that soft-collinear effective theory for processes involving both soft and collinear partons contains a new soft-collinear mode, which can communicate between the soft and collinear sectors of the theory. The…

Fairness and centredness of ideals in commutative rings, i.e., the relations between assassins and weak assassins of a module, its small or large torsion submodule, and the corresponding quotients, are studied. General criteria as well as…

This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach algebraic point of view. Namely, we mainly…

The theory of one-sided $M$-ideals and multipliers of operator spaces is simultaneously a generalization of classical $M$-ideals, ideals in operator algebras, and aspects of the theory of Hilbert $C^*$-modules and their maps. Here we give a…

A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined.…

We develop the integral calculus for quasi-standard smooth functions defined on the ring of Fermat reals. The approach is by proving the existence and uniqueness of primitives. Besides the classical integral formulas, we show the…

We define commutants mod normed ideals associated with compact smooth manifolds with boundary. The results about the K-theory of these operator algebras include an exact sequence for the connected sum of manifolds, derived from the…

Soft uniform structures provide a way to speak about uniform closeness in a parameterized setting. Working over a fixed parameter set, we treat entourages as soft relations and introduce a notion of \emph{soft uniformity} whose axioms…

Let $\Omega \subset \mathbb{R}^n $ be an open set, and let $\mathcal{E}(\Omega)$ be the ring of infinitely differentiable functions on $\Omega$. For an ideal $I \subset \mathcal{E}(\Omega)$, we denote by $Z(I)$ its zero set. A classical…

Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…

For self-adjoint operators $A, B$, a bounded operator $J$, and a function $f:\mathbb R\to\mathbb C$ we obtain bounds in quasi-normed ideals of compact operators for the difference $f(A)J-Jf(B)$ in terms of the operator $AJ-JB$. The focus is…

We obtain a complete characterization of the norm attainment set of a bounded linear functional on a normed space, in terms of a semi-inner-product defined on the space. Motivated by this result, we further apply the concept of…

We introduce the concept of a soft aura topological space $(X, \tilde{\tau}, \mathfrak{a}_E)$, obtained by equipping a soft topological space $(X, \tilde{\tau}, E)$ with a soft scope function $\mathfrak{a}_E : X \to \tilde{\tau}$ satisfying…

A sumset semigroup is a non-cancellative commutative monoid obtained from the sumset of finite non-negative integer sets. In this work, an algorithm for computing the ideals associated with some sumset semigroups is provided. Using these…

By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…