FUZZY COMPLEX GRASSMANNIAN SPACES AND THEIR STAR PRODUCTS

Fuzzy Complex Grassmannian Spaces and their Star Products

We derive an explicit expression for an associative star product on noncommutative versions of complex Grassmannian spaces, in particular for the case of complex 2-planes. Our expression is in terms of a finite sum of derivatives. This generalises previous results for complex projective spaces and gives a discrete approximation for the Grassmannians in terms of a non-commutative algebra, repres...

Fuzzy Complex Projective Spaces and their Star - products

We derive an explicit expression for an associative ∗-product on the fuzzy complex projective space, CPN−1 F . This generalises previous results for the fuzzy 2-sphere and gives a discrete non-commutative algebra of functions on CPN−1 F , represented by matrix multiplication. The matrices are restricted to ones whose dimension is that of the totally symmetric representations of SU(N). In the li...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Star Products on Generalised Complex Manifolds

We regard classical phase space as a generalised complex manifold and analyse the B–transformation properties of the ⋆–product of functions. The C–algebra of smooth functions transforms in the expected way, while the C–algebra of holomorphic functions (when it exists) transforms nontrivially. The B–transformed ⋆–product encodes all the properties of phase–space quantum mechanics in the presence...

Codes and designs in Grassmannian spaces