Vera Buryskova, Slavomir Burysek, Department of Mathematics, Faculty of Mechanical Engineering, Czech Technical University Prague, Karlovo nam. 13, 121 35 Praha 2, Czech Republic
Abstract: Notions as the numerical range $W(S,T)$ and the spectrum $\sigma(S,T)$ of couple $(S,T)$ of homogeneous operators on a Banach space are used to derive theorems on solvability of the equation $Sx-\lambda Tx=y.$ Conditions for the existence of eigenvalues of the couple $(S,T)$ are given.
Keywords: Banach and Hilbert space, homogeneous, polynomial, symmetric, monotone operator, numerical range, spectrum, eigenvalue.
Classification (MSC91): 47H15
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