Banach lattice

Definition. A multiplicative process is a one-parameter semigroup of bounded, non-negative linear transformations of a suitable Banach lattice if. 

The concept of Banach lattice arises from a slight extension of the concept of probability space already familiar in the theory of stochastic... 

Technically, if v(S) w(S) 0 implies t if . In general, the lattice property refers to the existence, for any two elements v and w, of a greatest lower bound V niW and a least upper bound v U w in Above, = v U 0 and v = v C 0. Unions and intersections define Boolean algebras as lattices with special additional properties. For the facts about Banach lattices needed here, see Garrett Birkhoff, Lattice theory, rev. ed.. New York, 1948, Chapter XV. 

In fact, the integral operators 8,A,F, etc., corresponding to successive events (scattering, absorption, fission, etc.) in a neutron life-history are not even singular, if one adopts modern mathematical techniques. They are bounded on the Banach lattice jSf—a fact which makes it easy to combine them. Technically, they form a Banach algebra [10], and one can write [2, (1)] ... 

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