Spectral properties of tensor products of linear operators. II. The approximate point spectrum and Kato essential spectrum

For tensor products of linear operators, their approximate point spectrum, approximate deficiency spectrum and essential spectra in the sense of T. Kato and Gustafson-Weidmann are determined together with explicit formulae for their nullity and deficiency. The theory applies to AI+IB and A B. Introduction. Given densely defined closed linear operators A and B in complex Banach spaces X and Y respectively with domains D[A] and D[B] and with nonempty resolvent sets p(A) and o(B), associated with each polynomial of degrees m in | and in tj (0.1) P(H,y)=2cJk?r1k jk is a polynomial operator (0.2) F {A I, I B } =^cjkAJ Bk jk in X a Y with domain D[Am] D[Bn]

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