Given two Banach spaces X and Y , we write L(X, Y ) for the space of all continuous linear operators from X to Y . A linear subspace J of L(X, Y ) is said to be an ideal if ATB ∈ J whenever A ∈ L(Y ), T ∈ J , and B ∈ L(X). It is known (see, e.g., Caradus:74 [CPY74]) that the only norm closed ideal in L(lp), 1 6 p < ∞ is the ideal of compact operators. The structure of closed ideals in L(lp ⊕ lq...

In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$  associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $  C^* $-algebra  $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...

In this paper, for any non-empty subset C of a pseudo BCI-algebra X, the concept of p-closure of C, denoted by C(pc), is introduced and some related properties are investigated. Applying this concept, a characterization of the minimal elements of X is given. It is proved that C(pc) is the least closed pseudo BCI-ideal of X containing C and K(X) for any ideal C of X...

An ideal I over Pκλ is said to be σ-strategically closed, proper or semiproper if the corresponding poset PI is σ-strategically closed, proper or semiproper, respectively. In this note we prove the following: • If there exists a σ-strategically closed, fine and κ-complete ideal over Pω2λ for some λ ≥ ω2 then ♦ω1 holds. • If there exists a proper, fine and κ-complete ideal over Pω2λ for some λ ≥...

In this paper, we apply the concept of an intuitionistic fuzzy set to closed ideals in BCI-algebras. The notion of an intuitionistic fuzzy closed ideal of a BCI-algebra is introduced, and some related properties are investigated. Characterizations of an intuitionistic fuzzy closed ideal are also given.

the goal of this paper is to generalize the recently introduced summability method and introduce double statistical convergence of order  by using ideal. we also investigate certain properties of this convergence.

With every σ-ideal I on a Polish space we associate the σ-ideal generated by closed sets in I. We study the forcing notions of Borel sets modulo the respective σ-ideals and find connections between their forcing properties. To this end, we associate to a σ-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of the...