The multiplication operator is a mathematical symbol or function used to indicate the operation of multiplying two or more numbers or variables. In most contexts, it is represented by the symbol "×" or "*". The multiplication operator can be used in arithmetic, algebra, and other areas of mathematics to combine values.
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For a finite almost-everywhere measurable function , the multiplication operator on L2 space has maximal operator domain . It is a closed operator: if and in L2 space, subsequences converge almost everywhere, giving . Its domain is dense, since truncating a function to the sets approximates it in L2 space. If is bounded, this is a bounded linear operator of norm equal to the essential supremum of .