This paper is a continuation of investigations of -inner product spaces given in [five, six, seven] and an extension of results given in [three] to arbitrary natural . It concerns families of projections of a given linear space onto its -dimensional subspaces and shows that between these families and -inner products there exist interesting close relations.
Contents Introduction 119 1. Quasiregular mappings 120 2. The Beltrami equation 121 3. The Beltrami-Dirac equation 122 4. A quest for compactness 124 5. Sharp -estimates versus variational integrals 125 6. Very weak solutions 128 7. Nonlinear commutators 129 8. Jacobians and wedge products 131 9. Degree formulas 134 References 136
Two new convergences of closed linear subspaces in the real separable Hilbert space are defined. These are the uniform strong convergence and the simultaneously strong and weak convergence to a single limit. Both convergences are characterized and it is shown that they verify the three axioms of Fréchet.
We present a new method for studying the numerical radius of bounded operators on Hilbert -modules. Our method enables us to obtain some new results and generalize some known theorems for bounded operators on Hilbert spaces to bounded adjointable operators on Hilbert -module spaces.