An Introduction to Banach Space Theory

By Robert E. Megginson. 1998

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Every Hilbert space is a Banach space, but the converse need not hold because a Banach space may have a norm that is not given by an inner product, e.g., the supremum norm ‖f‖ = supx∈X |f(x)| (Megginson 1998, Folland 1999).”
Misspecification in infinite-dimensional Bayesian statistics (2006, methodology): “ball Φ of L∞(X ,A,µ), which is dual to L1(X ,A,µ), since µ is σ-ﬁnite. If equipped with the weak-∗ topology, the positive unit ball Φ is Hausdorﬀ and compact by the Banach–Alaoglu theorem (see, e.g., [11], Theorem 2.6.18, and note that the positive functions form a closed and convex subset of the un”
Mann-Type Steepest-Descent and Modified Hybrid Steepest-Descent Methods for Variational Inequalities in Banach Spaces (2008, unknown): “R.E. Megginson (1998).”
Dependence of solutions and eigenvalues of measure differential equations on measures (2013, background): “For general theory on weak topologies and weak∗ topologies, we refer to [3,12].”
Hermite-Hadamard's Inequality and the p-HH-Norm on the Cartesian Product of Two Copies of a Normed Space (2010, unknown): “Note that Fr´echet diﬀerentiability implies Gˆateaux diﬀerentiability [23, p. 504], but not conversely.”
The Takagi function and its properties (Functions in Number Theory and Their Probabilistic Aspects) (2011, background): “(For a discussion of Schauder bases see Megginson [62, Sec.”
Distance-Based Classification with Lipschitz Functions (2004, background): “As the proof is a bit technical, we refer to Megginson (1998) for background reading.”