NORFOLK, Va. (AP) _ Defense lawyers in Arthur J. Walker's espionage trial rested their case without presenting any witnesses Thursday, after the judge denied their request to throw out the government's evidence.

U.S. District Judge J. Calvitt Clarke Jr., who is hearing the case without a jury, scheduled closing arguments Friday morning.

The prosecution rested earlier Thursday after reading grand jury testimony in which Walker said he took classified documents from his employer to prove to his brother he did not have access to highly sensitive information.

Walker faces seven espionage counts that accuse him of providing classified material to his brother John A. Walker Jr. for the Soviet Union.

In the grand jury testimony read by Assistant U.S. Attorney Michael Schatzow of Baltimore, Arthur Walker said his brother asked him to provide information for the Soviet Union in early 1980, shortly after a business they had started failed.

Walker admitted that he provided documents from his defense contractor employer, VSE Corp., to his brother and was paid $12,000.

''My real feeling was that if I could prove to him that I didn't have anything worthwhile, which he stated to me was the case, that I would not have to do anymore, and I could just shove it aside,'' Schatzow read from the transcript.

The prosecution's last witnesses were FBI agents who described John Walker's arrest in Maryland on May 20 and his relationship with his brother.

John Walker told a Soviet contact that Arthur could recognize unusual changes in schedules for Navy ship repairs, the agents said.

Papers found in John Walker's Norfolk home listed the name Art beside the code letter K, testified Paul Galvydis, an FBI agent in Norfolk.

A letter found with the classified materials was addressed ''Dear Friend'' and read in part, ''K and I have discussed your proposal and I will pass on some extensive details when we meet,'' testified Gerald B. Richards, an FBI agent in Washington, D.C.

''Briefly he is involved in carrier and amphibious ship maintenance planning. He would instantly recognize unrealistic repair schedules or see that ships were 'off their normal schedules,''' the letter went on. ''Otherwise he has no useful material.''

The letter also mentioned code letters the FBI has said stood for the other defendants in the alleged spy ring - John Walker's son, Navy Seaman Michael L. Walker, and Jerry A. Whitworth, an associate of John Walker.

John and Michael Walker are awaiting trial in Baltimore, and Whitworth is being held pending trial in San Francisco.

Richards testified a package found at the drop site where John Walker was spotted the evening of May 19 contained a four- to five-inch stack of documents, half classified secret and half confidential. The top document concerned the aircraft carrier USS Nimitz, he said.

Other agents described John Walker's arrest and the abrupt departure of a Soviet Embassy official a few days later.

Agent James L. Kolouch testified that John Walker was armed with a revolver when FBI agents confronted him in the seventh-floor lobby of a Rockville, Md., motel. After twice being ordered to drop the weapon, Walker complied and was searched by agents, Kolouch said.

Agent William H. Wang testified that Walker was holding a manila envelope containing instructions, maps of the area and photographs.

Other agents testified that Aleksey Tkachenko, vice consul at the Soviet Embassy in Washington, was seen driving in rural Maryland where John Walker allegedly made a drop of classified material.

Tkachenko and his family left their Alexandria aparment and flew out of National Airport a few days later, according to testimony.

The manager of the family's apartment complex, Joan Johnson, testified that they left food in the refrigerator and furniture in the apartment, including a mirror bearing a bumper sticker that read ''President Reagan.''