Equations with Operators Forming a Right Angle
نویسنده
چکیده
The operator B in a complex Hubert space H is said to form an angle Θ with the (stronger) operator A if D(A) c D(B) and, for every x in D(A), (Ax, Bx)π belongs to the cone K(θ) of all complex z with | arg (z) \ ̂ θ. If A and I? are closed maximal accretive operators and B forms a right angle with A, then A + JE> is closed maximal accretive and the Cauchy problem for each of the equations u(t) -f (A -f J5)u(ί) = /(£) and (I + B)u(t) + Au(ί) = /(£) is well-posed. Applications to partial differential equations are indicated in the second part.
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