**Albert "Tommy" Wilansky** (13 September 1921, St Johns, Newfoundland – 3 July 2017, Bethlehem, Pennsylvania) was a Canadian-American mathematician, known for introducing Smith numbers.^{[1]}^{[2]}

## Biography

Wilansky was educated as an undergraduate at Dalhousie University, where he received an M.A. in mathematics in 1944. From 1944 to 1947 he was a graduate student at Brown University.^{[3]} In 1947 he received his Ph.D. with advisor Clarence Raymond Adams and dissertation *An application of Banach linear functionals to the theory of summability*.^{[4]}

From 1948 until his official retirement in 1992, Wilansky was a faculty member of the mathematics department of Lehigh University.^{[3]}

He was the university’s Distinguished Professor of Mathematics for the final 14 years of his tenure. During his 44 years at Lehigh he was a Fulbright visiting professor several times, at universities in Reading (1972–1973), London (1973), Tel Aviv (1981), and Berne (1981). Outside of academia he was a consultant for the Frankford Arsenal for the year 1957–1958.

^{[3]}

Wilansky did research in analysis, specializing in summability theory, linear topological spaces, Banach algebras, and functional analysis.^{[3]} He was the author of several books and the author or co-author of more than 80 articles. He lectured at over 50 different universities.^{[2]} In 1969 he received the Mathematical Association of America's Lester R. Ford Award for his 1968 article *Spectral Decomposition of Matrices for High School Students*.^{[5]} (The 1969 award was also given individually to 5 other mathematicians.)

Wilansky was married to his first wife from 1947 until her death in 1969. They had two daughters. He had three step-daughters from his second marriage.

He was a professional musician for a brief time as a young man and continued playing piano and clarinet and writing songs, often with his wives and daughters.

^{[2]}

## Selected publications

### Articles

- Wilansky, Albert (1949). "An application of Banach linear functionals to summability".
*Transactions of the American Mathematical Society*.**67**(1): 59–68. doi:10.1090/S0002-9947-1949-0032025-7. ISSN 0002-9947. - —— (1949). "A necessary and sufficient condition that a summability method be stronger than convergence".
*Bulletin of the American Mathematical Society*.**55**(10): 914–916. doi:10.1090/S0002-9904-1949-09307-2. ISSN 0002-9904. - ——; Zeller, Karl (1955). "Summation of bounded divergent sequences, topological methods".
*Transactions of the American Mathematical Society*.**78**(2): 501–509. doi:10.1090/S0002-9947-1955-0067220-7. ISSN 0002-9947. - ——; Zeller, Karl (1963). "A biorthogonal system which is not a Toeplitz basis".
*Bulletin of the American Mathematical Society*.**69**(5): 725–726. doi:10.1090/S0002-9904-1963-11003-4. ISSN 0002-9904. - —— (1976). "On a characterization of barrelled spaces".
*Proceedings of the American Mathematical Society*.**57**(2): 375. doi:10.1090/S0002-9939-1976-0412761-2. ISSN 0002-9939. - Kalton, Nigel; —— (1976). "Tauberian operators on Banach spaces".
*Proceedings of the American Mathematical Society*.**57**(2): 251–255. doi:10.1090/S0002-9939-1976-0473896-1. ISSN 0002-9939. - Saxon, Stephen A.; —— (1977). "The equivalence of some Banach space problems".
*Colloquium Mathematicum*. Institute of Mathematics Polish Academy of Sciences.**37**(2): 217–226. doi:10.4064/cm-37-2-217-226. - Snyder, A. K.; —— (1980). "The Mazur-Orlicz bounded consistency theorem".
*Proceedings of the American Mathematical Society*.**80**(2): 374–376. doi:10.1090/S0002-9939-1980-0577777-5. ISSN 0002-9939. - —— (1981). "Mazur spaces".
*International Journal of Mathematics and Mathematical Sciences*.**4**: 39–53. doi:10.1155/S0161171281000021.

### Books

*Functional analysis*. New York: Blaisdell. 1964.*Topics in functional analysis*. Springer-Verlag. 1967; notes by W. D. LaverellCS1 maint: postscript (link) Wilansky, Albert (14 November 2006).*2006 pbk edition*. ISBN 978-3-540-35525-0.*Topology for analysis*. Waltham, Massachusetts: Ginn. 1970. Wilansky, Albert (2008).*Dover reprint*. ISBN 9780486469034.^{[6]}*Modern methods in topological vector spaces*. New York: McGraw-Hill. 1978.^{[7]}Wilansky, Albert (2013).*Dover reprint*. ISBN 9780486493534.^{[8]}*Summability through functional analysis*. North-Holland. 1984. Wilansky, A. (April 2000).*2000 pbk edition*. ISBN 9780080871967.

## References

**^**Wilansky, A. (1982). "Smith numbers".*Two-Year College Mathematics Journal*.**13**: 21. doi:10.2307/3026531. JSTOR 3026531.- ^
^{a}^{b}^{c}"Obituary. Albert Wilansky".*The Morning Call*. Allentown, Pennsylvania. July 11, 2017. - ^
^{a}^{b}^{c}^{d}Zitarelli, David E. "EPADEL: A Sesquicentennial History, 1926–2000". (See personal profile of Albert Wilansky in Chapter 6.) **^**Albert "Tommy" Wilansky at the Mathematics Genealogy Project**^**"Spectral Decomposition of Matrices for High School Students".*Mathematical Association of America*. (with link to PDF of article, which was published in*Mathematics Magazine*)**^**Stenger, Allen (October 10, 2009). "Review of*Topology for analysis*".*MAA Reviews, Mathematical Association of America*.**^**Retherford, James R. (1982). "Book Review:*Locally convex spaces*by H. Jarchow and*Modern methods in topological vector spaces*by Albert Wilansky".*Bulletin of the American Mathematical Society*.**7**(3): 612–615. doi:10.1090/S0273-0979-1982-15069-8. ISSN 0273-0979.**^**Stenger, Allen (April 6, 2015). "Review of*Modern Methods in Topological Vector Spaces"**.*MAA Reviews, Mathematical Association of America*.*