Vol. 45, No. 1, 1973

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Equations with operators forming a right angle

Ralph Edwin Showalter

Vol. 45 (1973), No. 1, 357–362

The operator B in a complex Hilbert space H is said to form an angle 𝜃 with the (stronger) operator A if D(A) D(B) and, for every x in D(A),(Ax,Bx)E belongs to the cone K(𝜃) of all complex z with |arg(z)|𝜃. If A and B are closed maximal accretive operators and B forms a right angle with A, then A + B is closed maximal accretive and the Cauchy problem for each of the equations u(t) + (A + B)u(t) = f(t) and (I + B)u(t) + Au(t) = f(t) is well-posed. Applications to partial differential equations are indicated in the second part.

Mathematical Subject Classification 2000
Primary: 47D05
Secondary: 47B44
Received: 10 December 1971
Published: 1 March 1973
Ralph Edwin Showalter