Dual space (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Dual space" in English language version.

refsWebsite

Global rank English rank

6^th place

5^th place

low place

archive.org

For $V^{\lor }$ used in this way, see An Introduction to Manifolds (Tu 2011, p. 19). This notation is sometimes used when $(\cdot )^{*}$ is reserved for some other meaning. For instance, in the above text, $F^{*}$ is frequently used to denote the codifferential of $F$ , so that $F^{*}\omega$ represents the pullback of the form $\omega$ . Halmos (1974, p. 20) uses $V'$ to denote the algebraic dual of $V$ . However, other authors use $V'$ for the continuous dual, while reserving $V^{*}$ for the algebraic dual (Trèves 2006, p. 35). Tu, Loring W. (2011). An Introduction to Manifolds (2nd ed.). Springer. ISBN 978-1-4419-7400-6. Halmos, Paul Richard (1974) [1958]. Finite-Dimensional Vector Spaces (2nd ed.). Springer. ISBN 0-387-90093-4. Trèves, François (2006) [1967]. Topological Vector Spaces, Distributions and Kernels. Mineola, N.Y.: Dover Publications. ISBN 978-0-486-45352-1. OCLC 853623322.
Rudin 1973, 3.1 Rudin, Walter (1973). Functional Analysis. International Series in Pure and Applied Mathematics. Vol. 25 (First ed.). New York, NY: McGraw-Hill Science/Engineering/Math. ISBN 9780070542259.
Rudin 1991, chapter 4 Rudin, Walter (1991). Functional Analysis. International Series in Pure and Applied Mathematics. Vol. 8 (Second ed.). New York, NY: McGraw-Hill Science/Engineering/Math. ISBN 978-0-07-054236-5. OCLC 21163277.

Tao, Terence (2012-12-29). "A mathematical formalisation of dimensional analysis". Similarly, one can define $V^{T^{-1}}$ as the dual space to $V^{T}$ ...

For $V^{\lor }$ used in this way, see An Introduction to Manifolds (Tu 2011, p. 19). This notation is sometimes used when $(\cdot )^{*}$ is reserved for some other meaning. For instance, in the above text, $F^{*}$ is frequently used to denote the codifferential of $F$ , so that $F^{*}\omega$ represents the pullback of the form $\omega$ . Halmos (1974, p. 20) uses $V'$ to denote the algebraic dual of $V$ . However, other authors use $V'$ for the continuous dual, while reserving $V^{*}$ for the algebraic dual (Trèves 2006, p. 35). Tu, Loring W. (2011). An Introduction to Manifolds (2nd ed.). Springer. ISBN 978-1-4419-7400-6. Halmos, Paul Richard (1974) [1958]. Finite-Dimensional Vector Spaces (2nd ed.). Springer. ISBN 0-387-90093-4. Trèves, François (2006) [1967]. Topological Vector Spaces, Distributions and Kernels. Mineola, N.Y.: Dover Publications. ISBN 978-0-486-45352-1. OCLC 853623322.
Narici & Beckenstein 2011, pp. 225–273. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Rudin 1991, chapter 4 Rudin, Walter (1991). Functional Analysis. International Series in Pure and Applied Mathematics. Vol. 8 (Second ed.). New York, NY: McGraw-Hill Science/Engineering/Math. ISBN 978-0-07-054236-5. OCLC 21163277.