We construct a sesquilinear form on the paragrassmann super disk, this form turns out positive over the quantum Bergman space. For this quantum Bergman space we obtain the reproducing kernels and the corresponding projections. We define Toeplitz operators which are l × l matrix such that their entries are Bergman-type operators over the unit disk.Keywords Toeplitz operators · Hilbert spaces with reproducing kernels · Operators in reproducing kernel Hilbert spaces · Groups and algebras in quantum theory
Mathematics Subject ClassificationPrimary 47B35; Secondary 46E22 · 47B32 · 81R05 To Sergei Grudsky on the occasion of his 60th birthday. B Armando Sánchez-Nungaray armsanchez@uv.mx Victor Pérez-García
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