COMPLEX POWERS OF $C$-SECTORIAL OPERATORS. PART I

Complex Powers of Operators

We define the complex powers of a densely defined operator A whose resolvent exists in a suitable region of the complex plane. Generally, this region is strictly contained in an angle and there exists α ∈ [0,∞) such that the resolvent of A is bounded by O((1 + |λ|)α) there. We prove that for some particular choices of a fractional number b, the negative of the fractional power (−A)b is the c.i....

Generation of Equicontinuous Semigroups by Hermitian and Sectorial Operators. I

Complex Powers of Nondensely Defined Operators

The power (−A)b, b ∈ C is defined for a closed linear operator A whose resolvent is polynomially bounded on the region which is, in general, strictly contained in an acute angle. It is proved that all structural properties of complex powers of densely defined operators with polynomially bounded resolvent remain true in the newly arisen situation. The fractional powers are considered as generato...

Theory of Operators Part I. Single Operators

The work of von Neumann on Operator Theory as distinct from the later work on Rings of operators, extends from 1928 to 1932 with certain later additions. I t is a remarkable development in which the inadequacy of formula mathematics for quantum mechanics was established and a new abstract approach introduced. This approach required the abstract definition of Hubert space and reformulation of th...

Sectorial Operators and Interpolation Theory

We present a survey of recent applications of interpolation ideas in the study of sectorial operators.