here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...

We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of “local system of vertex operators” for a (super) vector space. We first prove that any local system of vertex operators on a (super) vector space M has a natural vertex (super)algebra structure with M as a module. Then we prove that for a vertex (operat...

We prove a Lieb-Thirring type inequality for a complex perturbation of a d-dimensional massive Dirac operator Dm,m ≥ 0, d ≥ 1 whose spectrum is ] − ∞,−m] ∪ [m,+∞[. The difficulty of the study is that the unperturbed operator is not bounded from below in this case, and, to overcome it, we use the methods of complex function theory. The methods of the article also give similar results for complex...

Let A be a positive self-adjoint operator and let B be an m-accretive operator which is A-small with a relative bound less than one. Let H = A + B, then H is well-deened on dom(H) = dom(A) and m-accretive. If B is a strictly m-accretive operator obeying dom((H)) dom(A) \ dom((B)) 6 = f0g for some 2 (0; 1]; (1) then for the Trotter product formula we prove that ?

Ascending and descending Morse complexes are defined by the critical points and integral lines of a scalar field f defined on a manifold M . They induce a subdivision of M into regions of uniform gradient flow, thus providing a compact description of the topology of M and of the behavior of f over M . We represent the ascending and descending Morse complexes of f as a graph, that we call the Mo...

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 in their second dual. We show that several properties from the classical setting, like the stability under taking subspaces and quotients, unique extension proper...

Let (M,F) be a compact Riemannian foliated manifold, equipped with a bundlelike metric gM . We will also use the following notation: N ∗F is the conormal bundle to F , G is the holonomy groupoid of F . In Introduction, we will formulate our main results for the geometric case of the transverse signature operator, referring the reader to the main body of the paper for the formulations in the cas...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...

The states |α,m〉, defined as â†m|α〉 up to a normalization constant and m is a nonnegative integer, are shown to be the eigenstates of f(n̂,m)â where f(n̂,m) is a nonlinear function of the number operator n̂. The explicit form of f(n̂,m) is constructed. The eigenstates of this operator for negative values of m are introduced. The properties of these states are discussed and compared with those of th...