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Equations with
operators forming a right angle
Ralph Edwin Showalter |
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Vol. 45 (1973), No. 1, 357–362
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Abstract |
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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
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Milestones
Received: 10 December 1971
Published: 1 March 1973
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Authors |
| Ralph Edwin Showalter | |
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