High Quality Content by WIKIPEDIA articles! In mathematics, more specifically functional analysis and operator theory, the notion of unbounded operator provides an abstract framework for dealing with differential operators, unbounded observables in quantum mechanics, and other cases. The term "unbounded operator" can be misleading, since * "unbounded" should be understood as "not necessarily bounded"; * "operator" should be understood as "linear operator" (as in the case of "bounded operator"); * the domain of the operator is a linear subspace, not necessarily the whole space (in contrast to "bounded operator"); * this linear subspace is not necessarily closed; often (but not always) it is assumed to be dense; * in the special case of a bounded operator, still, the domain is usually assumed to be the whole space. In contrast to bounded operators, unbounded operators on a given space do not form an algebra, nor even a linear space, because each one is defined on its own domain.

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