Operator factorization of range space relations?

Locating the Range of an Operator on a Hilbert Space

exists (is computable) for each x in H; if P is that projection, / is the identity operator on H, and the adjoint T*ofT exists, then / P is the projection of H on ker(3*), the kernel of T*. (For an example to show that the existence of the adjoint of a bounded operator on a Hilbert space is not automatic in constructive mathematics, see Brouwerian Example 3 in [7]; see also Example 2 below.) Th...

On the Operator Algebra for the Space-time Uncertainty Relations

The purpose of this note is to show that the construction of the C-algebra for the space-time uncertainty relations which was introduced by Doplicher, Fredenhagen and Roberts [2,3,4] fits comfortably into the deformation quantization framework developed in [5]. This has the mild advantages that one can work directly with functions on space-time rather than with their Fourier transforms, the tre...

Shape Operator of Slant Submanifolds in Kenmotsu Space Forms

Hypersurfaces of a Sasakian space form with recurrent shape operator

Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.

Factorization of Twist-Four Gluon Operator Contributions

We consider diagrams with up to four t-channel gluons in order to specify gluonic twist-four contributions to deep inelastic structure functions. This enables us to extend the method developed by R.K.Ellis, W.Furmanski, and R. Petronzio (EFP) [1] to the gluonic case. The method is based on low-order Feynman diagrams in combination with a dimensional analysis. It results in explicitly gauge inva...