Jay Solomon, who became administrator of the General Services Administration in May, says he owes his appointment to the volunteer campaign work of his son and daughter.

Joel Solomon, who works on a ranch in Jackson Hole, Wyo., and Linda Solomon, a student at Northwestern University, both had active roles in the Carter campaign.

"That's how I came to be noticed by the Carter people who were involved in top staffing for the new administration," recalled the man now charged with overseeing the real estate and housekeeping needs of the U. S. government.

To the top post of GSA, which has more than 37,000 employees, Solomon brings a background that includes executive experience with Arlen Shopping Centers Co. and other Arlen realty interests.

The 55-year-old native of Chattanooga is a graduate of Vanderbilt University who once worked for the chain of motion picture theaters founded by his father.

When a drive-in theater was destroyed by a widnstorm in 1961, Solomon sold the theater chain and built the Eastgate Shopping Center on a 55-acre tract in Chattanooga.This was followed by additional shopping centers and the founding of Arlen Shopping Centers. When Solomon resigned from Arlen Realty & Development Corp. to go to GSA, the firm owned or managed 184 such commercial centers.

Interested in Democratic politics most of his life, Solomon also has been heavily involved in civic and charitable activities in Tennessee. He was chairman of the Chattanooga Housing Authority and a board member for 14 years. The GSA chief has attended a number of cabinet meetings, unlike most of his predecessors, and is said to have a strong recognition factor inside the White House. Some Tennessee newspapers are suggesting that he be appointed to replace Bert Lance as head of the Office of Management and Budget.

As head of GSA, Solomons says he has a mandate from President Carter to concentrate on preserving buildings, leasing space when it is needed and building it only as an alternative. Solomon has also has taken steps to implement energy efficiency in older federal buildings.

Solomon and his wife, Rosalind Fox, who is a professional photographer, are leasing an apartment in The Plaza, a luxury condominium opposite the Watergate complex in the Foggy Bottom area of Washington.