inf u 6 Ttu(x) 6 u(x) 6 Ťtu(x) 6 supu for each t > 0 and each x ∈ H. A function u : H −→ R is called k-semi-concave, k > 0, if the function x −→ u(x)−‖x‖2/k is concave. The function u is called k-semi-convex if −u is k-semiconcave. A bounded function u is t-semi-concave if and only if it belongs to the image of the operator Tt, this follows from Lemma 1 and Lemma 3 below. A function is called s...

or171algebra12, 25adapted to typed set150associated37, 43, 150, 152bottomed58category-based126containing a typed set37disjoint from a typed set46extension of46free37functionally free145, 147functional145, 147ground term56heterogenous54initial12, 33initial completion of104<...

We investigate a connection between distance-regular graphs and Uq (sl(2)), the quantum universal enveloping algebra of the Lie algebra sl(2). Let 0 be a distance-regular graph with diameter d ≥ 3 and valency k ≥ 3, and assume0 is not isomorphic to the d-cube. Fix a vertex x of0, and let T = T (x) denote the Terwilliger algebra of 0 with respect to x . Fix any complex number q 6∈ {0, 1,−1}. The...

In this note we show that an unbounded regular operator t on Hilbert C∗modules over an arbitrary C∗ algebra A has polar decomposition if and only if the closures of the ranges of t and |t| are orthogonally complemented, if and only if the operators t and t∗ have unbounded regular generalized inverses. For a given C∗-algebra A any densely defined A-linear closed operator t between Hilbert C∗-mod...

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

The notion of a quasi-free Hilbert module over a function algebra A consisting of holomorphic functions on a bounded domain Ω in complex m space is introduced. It is shown that quasi-free Hilbert modules correspond to the completion of the direct sum of a certain number of copies of the algebra A. A Hilbert module is said to be weakly regular (respectively, regular) if there exists a module map...

In this paper several results of N. Noble concerning closed projections are extended using generalizations of first countable, Frechet, and sequential spaces. We also consider compactness conditions defined by requiring that certain nets have cluster points.

It is shown that the initial value problem (IVP) of the generalized KdV equation @tu + @x(a(u)) + @ 3 xu = 0; u(x; 0) = (x) is well posed in the classical Sobolev space H(R) with s > 3=4, which thus establishes a nonlinear map K from H(R) to C([ T; T ];H(R)). Then it is proved that (i) if a = a(x) is a C function on R to R, then K is in nitely many times Frechet di erentiable; (ii) if a = a(x) ...

Let G be a connected reductive p-adic group and let g be its Lie algebra. LetO be a G-orbit in g. Then the orbital integral μO corresponding to O is an invariant distribution on g, and Harish-Chandra proved that its Fourier transform μ̂O is a locally constant function on the set g′ of regular semisimple elements of g. Furthermore, he showed that a normalized version of the Fourier transform is l...

and similarly for the right topological centre Z(r)(A′′). The algebra A is said to be Arens regular if Z(`)(A′′) = Z(r)(A′′) = A′′ and strongly Arens irregular if Z(`)(A′′) = Z(r)(A′′) = A. For example, every C∗-algebra is Arens regular [2]. There has been a great deal of study of these two algebras, especially in the case where A is the group algebra L(G) for a locally compact group G. Results...