one can quantize an invertible symbol σ ∈ C∞(S∗X; hom(π∗E, π∗F )) as an elliptic pseudodifferential operator in the Φ-b or edge calculus, ΨΦ-b(X;E,F ), introduced in [7] or alternately as an elliptic operator in the Φ-c or φ calculus, ΨΦ-c(X;E,F ), introduced in [8]. As on a closed manifold, either of these operators will induce a bounded operator acting between natural L-spaces of sections but...

and this index is constant on continuous families of such L. Suppose that D is an elliptic operator of order m on sections of a vector bundle E± over a smooth, compact manifold M . Let H (Γ (M,E±)) denote the Sobolev s-norm completion of the space of sections Γ (M,E), with respect to a chosen metric. Then D can be extended to be a bounded linear operator Ds : H s (Γ (M,E)) → Hs−m (Γ (M,E−)) tha...

 For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto  fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an o...

In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...

We consider the function class E generated by the constant functions, the projection functions, the predecessor function, the substitution operator, and the recursion on notation operator. Furthermore, we introduce regressive machines, i.e. register machines which have the division by 2 and the predecessor as basic operations. We show that E is the class of functions computable by regressive ma...

Let T : C(S) → C(S) be a bounded linear operator. We present a necessary and sufficient condition for the so-called Daugavet equation ‖Id+ T ‖ = 1 + ‖T ‖ to hold, and we apply it to weakly compact operators and to operators factoring through c0. Thus we obtain very simple proofs of results by Foiaş, Singer, Pe lczyński, Holub and others. If E is a real Banach space, let us say that an operator ...

We revisit Khudaverdian’s geometric construction of an odd nilpotent operator ∆E that sends semidensities to semidensities on an antisymplectic manifold. We find a local formula for the ∆E operator in arbitrary coordinates and we discuss its connection to Batalin-Vilkovisky quantization. MCS number(s): 53A55; 58A50; 58C50; 81T70.

We prove that the operator Hilbert space OH does not embed completely isomorphically into the predual of a semi-finite von Neumann algebra. This complements Junge’s recent result that it admits such an embedding in the non semi-finite case. ——————– In remarkable recent work [5], Marius Junge proves that the operator Hilbert space OH (from [8], see also [9]) embeds completely isomorphically (c.i...

this paper presents characterizations of m-fuzzifying matroids bymeans of two kinds of fuzzy operators, called m-fuzzifying derived operatorsand m-fuzzifying difference derived operators.

The theory of translation-invariant operators on various spaces of functions (or measures or distributions) is a well-trodden field. The problem is to decide, first, whether or not a linear operator between two function spaces on, say, IR or R + which commutes with one or many translations on the two spaces is necessarily continuous, and, second, to give a canonical form for all such continuous...