Bounded linear maps commute with Bochner integration

Depends on

• Bochner-integrable function
• A bounded linear operator between normed spaces
• The Banach-valued simple integral is well defined

Used by

• Parseval and Fourier inversion for compact groups Corollary
• Spatial smoothing of forcing separated from the observation time Corollary
• Infinitely many modes admit inequivalent irreducible regular Weyl representations Counterexample
• Partially one-homogeneous signed measure projection Definition
• Relaxed objective for a partially one-homogeneous projection Definition
• The Duhamel heat potential Definition
• A trace-class Gaussian with full support and a proper Cameron–Martin space Example
• Spectral projection of an isolated eigenvalue agrees with the riesz projection Example
• The right-translation semigroup on Lp has the weak derivative as generator Example
• A positive rank-one Haar average is a nonzero compact intertwiner Lemma
• A system of imprimitivity integrates to a nondegenerate representation of the transformation algebra Lemma
• A weak two-homogeneous projection limit is stationary on its support Lemma
• Characters of the L1 algebra of an abelian group Lemma
• Feature and energy identities for homogeneous projections Lemma
• Feature energy is W2-continuous on a common cutoff Lemma
• Finite partition energy yields Hilbert-valued AC2 paths Lemma
• First variation and optimality over nonnegative measures Lemma
• Independent centered Hilbert-valued elements have zero expected inner product Lemma
• Integrated pressure recovery and MINI pressure-primitive convergence Lemma
• Laplace resolvents of a unitary group Lemma
• Laplace uniqueness identifies two exponentially bounded semigroups Lemma
• Long-run covariance of an L2-m-approximable shift is trace class Lemma
• Nonzero multiplicative functionals on L¹ of an LCA group are Fourier evaluations Lemma
• Partial feature flows have exact energy and weight-moment identities Lemma
• Partial one-homogeneous energy is continuous under W2 convergence Lemma
• Recovering a unitary group representation from a nondegenerate L one representation Lemma
• RNP is invariant under Banach-space isomorphism Lemma
• RNP is separably determined Lemma
• Signwise first-variation conditions minimize the relaxed objective Lemma
• Smooth and K-finite vectors are dense and stable under the derived action Lemma
• Spectral measure of a unitary representation of an abelian group, covariance, and ergodicity Lemma
• The Gaussian Weyl average is a rank-one projection Lemma
• The Hilbert lift induces the localized Wasserstein continuity equation Lemma
• The L1 action of a strongly continuous unitary representation Lemma
• The localized lifted feature energy is semiconvex Lemma
• The weighted discrete-series space is a Hilbert space with K-type basis Lemma
• Time derivatives of fixed and differentiable comparison projections Lemma
• Time integrals of semigroup orbits lie in the generator domain Lemma
• Time mollification preserves the evolution-space derivative Lemma
• Weighted Hilbert Gaussian series and prior regularity Lemma

…and 10 more results.

Dependency tree · two levels

10 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• Gerald Teschl, Topics in Real and Functional Analysis (standard reference, not scraped)