In the present paper, we consider a 2 ? block operator matrices with unbounded entry operators acting on Banach spaces. Under some conditions, develop criteria for its self-adjointness and closedness. The obtained results are applied to an Hamiltonian matrix.

In this paper we introduce a definition of gradation of continuity ingraded fuzzy topological spaces and study its various characteristic properties.The impact of the grade of continuity of mappings over the N-compactnessgrade is examined. Concept of gradation is also introduced in openness, closed-ness, homeomorphic properties of mappings and T2 separation axiom. Effectof the grades interrelat...

Let X be a Banach space and T bounded linear operator acting in lp(ℤc,X), 1 ≤ p ∞. The is called locally nuclear if it can represented the form $${(Tx)_k} = \sum\limits_{m \in {\mathbb{Z}^c}} {{b_{km}}} {x_{k - m}},\quad k {\mathbb{Z}^c},$$ where bkm: → are nuclear, $${\left\| \right\|_{{\mathfrak{S}_1}}} \le {\beta _m},\quad k,m $$\left\|\cdot\right\|{_{{\mathfrak{S}_1}}}$$ norm, β ∈ l1(ℤc,ℂ) ...