In this paper, we generalize to Frobenius-Weil bundles some lifts of symplectic manifolds and symplectic vector bundles.

In this paper, we investigate a new class of unbounded linear operators, that is, the unbounded generalized B-Fredholm operators in Banach space. More explicitly, we provide a characterization of this class of operators and some of its basic properties on a Banach space. Moreover, we study the generalized B-Fredholm spectrum and we prove a perturbation result of an unbounded generalized B-Fredholm operator under a commuting power finite-rank operator.

We give an elementary method for constructing commutative Fréchet algebras with non-unique Fréchet algebra topology. The result is applied to show that the action of any non-algebraic analytic function may fail to be uniquely defined among other useful applications. We give an affirmative answer to a question of Loy (1974) for Fréchet algebras. We also obtain the uniqueness of the Fréchet algebra topology of certain Fréchet algebras with finite dimensional radicals.

Let G be a closed symmetric monoidal concrete Grothendieck category. In this paper, we introduce a model structure on (CN (G), P⊗dw ) the exact category of N -complexes with the degree-wise ⊗-pure exact structure. Our result is based on the Gillespie’s Theorem by introducing two compatible cotorsion pairs on this category.

A progress report on the (still unresolved) Landsberg-Berwald problem of Finsler geometry: whether there can be non-Berwaldian regular Landsberg spaces.

For any Boolean space X and a discrete almost distributive lattice D, it is proved that the set C(X, D) of all continuous mappings of X into D, when D is equipped with the discrete topology, is an almost Boolean algebra under pointwise operations. Conversely, it is proved that any almost Boolean algebra is a homomorphic image of C(X,D) for a suitable Boolean space X and a discrete almost distributive lattice D.

Let H be a Hilbert space. In this paper we show among others that, if f, g are continuous on the interval I with 0 <γ ≤ f(t)/g(t)≤ Γ for t ∈ I and if A and B are selfadjoint operators with Sp (A), Sp (B) ⊂ I, then [f1−ν(A) gν (A)] ⊗ [fν(B) g1−ν (B)] ≤ (1 − ν) f (A) ⊗ g (B) + ν g (A) ⊗ f (B) ≤ [(γ + Γ) 2/4γΓ]R [f1−ν(A) gν (A)] ⊗ [fν(B) g1−ν (B)]. The above inequalities also hold for the Hadamard product “ ◦ ” instead of tensorial product “ ⊗ ”.

Let R be a prime ring of characteristic not 2 and U be a noncentral square closed Lie ideal of R. An additive mapping H on R is called a homoderivation if H(xy) = H(x)H(y)+H (x) y+xH(y) for all x, y ∈ R. In this paper we investigate homoderivations satisfying certain differential identities on square closed Lie ideals of prime rings.

We determine several classes of continua whose hyperspaces of subcontinua are infinite dimensional and homeomorphic to cones over (usually) other continuum. In particular, we obtain many Peano continua with such a property.

We study measurable spaces equipped with a σ-ideal of negligible sets. We find conditions under which they admit a localizable locally determined version – a kind of fiber space that locally describes their directions – defined by a universal property in an appropriate category that we introduce. These methods allow to promote each measure space (X, A , µ) to a strictly localizable version (X̂, Â, µ̂), so that the dual of L1 (X, A , µ) is L∞ (X̂, Â, µ̂). Corresponding to this duality is a generalized Radon-Nikodým theorem. We also provide a characterization of the strictly localizable version in special cases that include integral geometric measures, when the negligibles are the purely unrectifiable sets in a given dimension.