urn:taro:utexas.cah.00454 A Guide to the B. J. Pettis Papers, 1938-1980 20 October 2005Encoded in XMetal 2 by Nikki Thomas according to instructions in TARO 2 EAD 2002 Editing Instructions. Descriptive Summary Pettis, B. J. B. J. Pettis Papers 1938-1980Materials are written in English. 2005-204 1 ft., 6 in. Archives of American Mathematics, Center for American History,The University of Texas at Austin Billy James (B. J.) Pettis (1913-1979) received his Ph.D. in 1937 from the University of Virginia. Pettis was first a Professor of Mathematics at Tulane University and then at the University of North Carolina at Chapel Hill from 1957 until his death in 1979. This collection primarily consists of annotated reprints, mathematical notes, lecture notes, and subject files. Biographical Note

Billy James (B. J.) Pettis (1913-1979) received his Ph.D. in 1937 from the University of Virginia. Pettis was first a Professor of Mathematics at Tulane University and then at the University of North Carolina at Chapel Hill from 1957 until his death in 1979. Pettis produced fundamental work in functional analysis, including the general theory of Pettis Integration that is used in control theory and areas of pure mathematics. Pettis is also known for the Orlicz-Pettis Theorem, the Dunford-Pettis Theorem, and the Pettis Theorem on Measurability.

 Scope and Contents

This collection primarily consists of annotated reprints, mathematical notes, lecture notes, and subject files.

Forms part of the Archives of American Mathematics

 Access Restrictions

Unrestricted access

 Preferred Citation

B. J. Pettis Papers, 1938-1980, Archives of American Mathematics, the Dolph Briscoe Center for American History, The University of Texas at Austin.

 Index Terms Pettis, Billy James University of North Carolina at Chapel Hill. Dept. of Mathematics. Detailed Description of the Papers 4RM139 General correspondence, 1975 and undated Works by Pettis: 4RM139 “Closed Graph and Open Mapping Theorem in Metrically Complete Spaces” [includes drafts and notes], undated 4RM139 Duke talk, “Open Mapping and Closed Graph Theorems; or Ancient Monuments Revisited,” North Carolina Analysis Colloquium [includes draft copies and notes], 1971-1975 and undated 4RM139 “On Some Theorems of Sierpinski on Subalgebras of Boolean σ-Rings” by B. J. Pettis [annotated reprint with separate notes], 1970 and undated 4RM167 “S – G – P Seminar: 20 Jan 1977. Difference Theorems, and Gelfand’s 1935 Lemma and Some of Its Recent Successors” [photocopy of handwritten manuscript], 1977 4RM167 “On the Radon-Nikodym Theorem” [typescript], undated 4RM167 “Open Homomorphisms via Somewhere Denseness” [typescript], undated 4RM167 “Some Topological Questions Related to Open Mapping and Closed Graph Theorems” in Studies in Topology, New York: Academic Press, Inc., 1975 4RM167 Reprints: 4RM167 “A Note on Regular Banach Spaces,” in Bulletin of the American Mathematical Society, June 1938 4RM167 “Linear Functions and Completely Additive Set Functions,” in Duke Mathematical Journal, 4 (3), September, 1938 4RM167 “On Integration in Vector Spaces,” in Transactions of the American Mathematical Society, 44 (2), September 1938 4RM167 “Differentiation in Banach Spaces,” in Duke Mathematical Journal, 5 (2), June, 1939 4RM167 “A Proof that Every Uniformly Convex Space is Reflexive” in Duke Mathematical Journal, 5 (2), June 1939 4RM167 “Linear Operations Among Summable Functions,” in Proceedings from the National Academy of Sciences, 25 (10), October, 1939 4RM167 “Linear Operations on Summable Functions,” Transactions of the American Mathematical Society, 47 (3), May, 1940 4RM167 “On Continuity and Openness of Homomorphisms in Topological Groups,” in Annals of Mathematics, 52 (2), September 1950 4RM167 “Remarks on a Theorem of E. J. McShane” in Proceedings of the American Mathematical Society, 2 (1), February, 1951 4RM167 “On the Continuity of Parametric Linear Operations” in Proceedings of the American Mathematical Society, 2 (3), June, 1951 4RM167 “On the Extension of Measures” in Annals of Mathematics, 54 (1), July, 1951 4RM167 “Uniform Cauchy Points and Points of Equicontinuity” in American Journal of Mathematics, 73 (3), July, 1951 4RM167 “Notes on Measure Theorey: Part 1. Lattices and Lattice Functionals,” Technical Report No. 2, Prepared under Contract N7-ONR-434 Task Order III for Office of Naval Research. Department of Mathematicas, Tulane University August 1, 1951 4RM167 “A Note on Everywhere Dense Subgroups,” Proceedings of the American Mathematical Society, 3 (2), April, 1952 4RM167 “Comments on Open Homomorphisms,” in Proceedings of the American Mathematical Society, 8 (3), June, 1957 4RM167 “On a Vector Space Construction by Hausdorff,” in Proceedings of the American Mathematical Society, 8 (3), June, 1957 4RM167 “A Comment on Compactness,” in American Mathematical Monthly, 75 (5), May, 1968 4RM167 “Award for Distinguished Service to Professor Edward G. Begle,” in American Mathematical Monthly, 76 (1), January, 1969 4RM167 “Cluster Sets of Nets,” in Proceedings of the American Mathematical Society, 22 (2), August, 1969 4RM167 “On Nikaidô’s proof of the invariant mean-value theorem,” in Studia Mathematica, T. XXXIII, 1969 4RM167 “On Some Theorems of Sierpinski on Subalgebras of Booleans [sigma]-Rings” in Bulletin de L’Academie Polonaise des Sciences, 19 (7), 1971 4RM167 “Closed Graph and Open Mapping Theorems in Certain Topologically Complete Spaces,” in Bull. London Math. Soc., 6 [includes typescript with corrections and annotated preprint], 1974 4RM167 “Addition to the Note: Closed Graph and Open Mapping Theorems in Certain Topologically Complete Spaces,” in Bull. London Math. Soc., 7, 1975 4RM167 4RM167 4RM167 4RM167 4RM167 4RM167 Works not by Pettis: 4RM139 Reprints [with annotations by Pettis]: 4RM139 “Théorie des sous – Mesures application a l’intégration vectorielle” by Jean-Claude Massé [includes correspondence], 1974-1975 and undated 4RM139 American Mathematical Monthly 8(4), April 1973 [includes mathematical notes], 1951, 1973 and undated 4RM139 “On Infinite-dimensional Linear Spaces” by G. W. Mackey, 1945 4RM139 “Prolongement des Mesures Vectorielles” by Gr. Arsene and S. Stratila, 1965 4RM139 “Applications of Almost Periodic Compactifications” by Karel Deleeuw and Irving Glicksburg, 1961 and undated 4RM139 “Stefan Banach - exposé fait par M. H. Steinhaus le 4 septembre 1960 à Varsovie à l’occasion de la Conférence de l’Analyse Fonctionnelle,” 1960 4RM139 “Generalized Means” by F. B. Wright in Transactions of the AMS, 98 (2), 187-203, 1961 4RM139 Proceedings on the Symposium on Spectral Theory and Differential Problems, 1951 and undated 4RM139 Assorted reprints [photocopies], 1957-1972 Lecture notes: 4RM139 Carl Pearcy [“Some Recent Developments in Operator Theory”], undated 4RM166 Rings of operators notes by Irving Kaplansky, 1955 4RM166 Topological algebra notes by Irving Kaplansky, 1952 and undated 4RM166 “The Revolution in Mathematics” by Marshall Stone, 1961 4RM166 G. Whaples [includes algebraic number theory and class field theory lectures], 1964-1965 and undated Subject files: 4RM166 Closed graphs, etc., 1970-1973 and undated 4RM166 Cluster sets, 1948, 1971 and undated 4RM166 Continuity stuff [includes correspondence with H. E. White, Jr., a reprint of “On the Continuity of Parametric Linear Operations” by Pettis, and mathematical work], 1951-1972 and undated 4RM166 Difference theorems, 1977-1978 and undated 4RM166 Differentiation, 1968-1971 and undated 4RM138 Generalized convexity, 1956-1973 and undated 4RM138 Integration, 1973 and undated 4RM167 Pettis memorial [includes biographical information], 1978-1979 and undated 4RM167 Pettis conference [includes correspondence], 1979-1980 and undated 4RM138 La Géométrie des Groupes Classiques by Jean Dieudonné [photocopy], 1963 4RM138 [Unfoldered mathematical notes], 1967-1977 and undated 4RM167 Index cards of bibliographic citations [some include annotations, approximately 3 inches], undated