Abstract
Let X be a Banach space. A one parameter family T(t), 0 ≤t < ∞, of bounded linear operators from X into X is a semigroup of bounded linear operators on X if
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(i)
T(0) = I, (I is the identity operator on X).
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(ii)
T(t + s) = T, (t)T(s) for very t, s ≥ 0 (the semigroup property).
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© 1983 Springer-Verlag New York, Inc.
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Pazy, A. (1983). Generation and Representation. In: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, vol 44. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5561-1_1
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DOI: https://doi.org/10.1007/978-1-4612-5561-1_1
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